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PAYNE</span></p> + + + + +<p class="nindc space-above2 space-below2"> +PUBLISHED BY THE OBSERVATORY<br> +CAMBRIDGE, MASSACHUSETTS<br> +1925 +</p></div> + +<hr class="chap x-ebookmaker-drop"> + +<div class="chapter"> + +<p class="nindc"> +COPYRIGHT, 1925<br> +BY HARVARD OBSERVATORY</p> + +<p class="nindc space-above2 space-below2"> +PRINTED AT THE HARVARD UNIVERSITY PRESS<br> +CAMBRIDGE, MASS., U.S.A.<br> +</p></div> + +<hr class="chap x-ebookmaker-drop"> + +<div class="chapter"> +<p><span class="pagenum" id="Page_v">[Pg v]</span></p> + +<h2 class="nobreak" id="EDITORS_FOREWORD">EDITOR’S FOREWORD</h2> +</div> + + +<p class="nind"> +THE most effective way of publishing the results of astronomical +investigations is clearly dependent on the nature and scope of each +particular research. The Harvard Observatory has used various forms. +Nearly a hundred volumes of Annals contain, for the most part, tabular +material presenting observational results on the positions, photometry, +and spectroscopy of stars, nebulae, and planets. Shorter investigations +have been reported in Circulars, Bulletins, and in current scientific +journals from which Reprints are obtained and issued serially.</p> + +<p>It now appears that a few extensive investigations of a somewhat +monographic nature can be most conveniently presented as books, the +first of which is the present special analysis of stellar spectra by +Miss Payne. Other volumes in this series, it is hoped, will be issued +during the next few years, each dealing with a subject in which a +large amount of original investigation is being carried on at this +observatory.</p> + +<p>The Monographs will differ in another respect from all the publications +previously issued from the Harvard Observatory—they cannot be +distributed gratis to observatories and other interested scientific +institutions. It is planned, however, to cover a part of the expenses +of publication with special funds and to sell the volumes at less than +the cost of production.</p> + +<p>The varied problems of stellar atmospheres are particularly suited to +the comprehensive treatment here given. They involve investigations of +critical potentials, spectral classification, stellar temperatures, +the abundance of elements, and the far-reaching theories of thermal +ionization as developed in the last few years by Saha and by Fowler and +Milne. Some problems of special interest to chemists and physicists are +considered, and subjects intimately bound up with inquiries concerning +stellar evolution come under discussion.</p> + +<p><span class="pagenum" id="Page_vi">[Pg vi]</span></p> + +<p>The work is believed to be fairly complete from the bibliographic +standpoint, for Miss Payne has endeavored throughout to give a synopsis +of the relevant contributions by various investigators. Her own +contributions enter all chapters and form a considerable portion of +Parts II and III.</p> + +<p class="space-above2"> +It should be remembered that the interpretation of stellar spectra from +the standpoint of thermal-ionization is new and the methods employed +are as yet relatively primitive. We are only at the beginning of the +astronomical application of the methods arising from the newer analyses +of atoms. Hence we must expect (and endeavor to provide) that a study +such as is presented here will promptly need revision and extension in +many places. Nevertheless, as it stands, it shows the current state +of the general problem, and will also serve, we hope, as a summary of +past investigations and an indication of the direction to go in the +immediate future.</p> + +<p>In the course of her investigation of stellar atmospheres, Miss Payne +has had the advantage of conferences with Professors Russell and +Stewart of Princeton University and Professor Saunders of Harvard +University, as well as with various members of the Harvard Observatory +staff.</p> + +<p>The book has been accepted as a thesis fulfilling the requirements for +the degree of Doctor of Philosophy in Radcliffe College.</p> + +<p style="text-align:right">H. S.</p> + +<p>MAY 1, 1925.</p> + + +<hr class="chap x-ebookmaker-drop"> +<p><span class="pagenum" id="Page_vii">[Pg vii]</span></p> + +<div class="chapter"> +<h2 class="nobreak" id="CONTENTS">CONTENTS</h2> +</div> + +<table class="autotable"> +<tbody><tr> +<td class="tdc" colspan="2">PART I</td> +</tr><tr> +<td class="tdc" colspan="2">THE PHYSICAL GROUNDWORK</td> +</tr><tr> +<td class="tdl"><span class="allsmcap">I. THE LABORATORY BASIS OF ASTROPHYSICS</span></td> +<td class="tdr"><a href="#Page_3">3</a></td> +</tr><tr> +<td class="tdlh">Relation of physics to astrophysics.<br> +<span class="tdlh">Properties of matter associated with nuclear structure.</span><br> +<span class="tdlh">Arrangement of extra-nuclear electrons.</span><br> +<span class="tdlh">Critical potentials.</span><br> +<span class="tdlh">Duration of atomic states.</span><br> +<span class="tdlh">Relative probabilities of atomic states.</span><br> +<span class="tdlh">Effect on the spectrum of conditions at the source.</span><br> +<span class="tdlh2">(<i>a</i>) Temperature class.</span><br> +<span class="tdlh2">(<i>b</i>) Pressure effects.</span><br> +<span class="tdlh2">(<i>c</i>) Zeemann effect.</span><br> +<span class="tdlh2">(<i>d</i>) Stark effect.</span></td> +<td></td> +</tr><tr> +<td class="tdl"><span class="allsmcap">II. THE STELLAR TEMPERATURE SCALE</span></td> +<td class="tdr"><a href="#Page_27">27</a></td> +</tr><tr> +<td class="tdlh">Definitions.<br> +<span class="tdlh">The mean temperature scale.</span><br> +<span class="tdlh">Temperatures of individual stars.</span><br> +<span class="tdlh">Differences in temperature between giants and dwarfs</span><br> +<span class="tdlh">The temperature scale based on ionization.</span></td> +<td></td> +</tr><tr> +<td class="tdl"><span class="allsmcap">III. PRESSURES IN STELLAR ATMOSPHERES</span></td> +<td class="tdr"><a href="#Page_34">34</a></td> +</tr><tr> +<td class="tdlh">Range in stellar pressures.<br> +<span class="tdlh">Measures of pressure in the reversing layer.</span><br> +<span class="tdlh2">(<i>a</i>) Pressure shifts of spectral lines.</span><br> +<span class="tdlh2">(<i>b</i>) Sharpness of lines.</span><br> +<span class="tdlh2">(<i>c</i>) Widths of lines.</span><br> +<span class="tdlh2">(<i>d</i>) Flash spectrum.</span><br> +<span class="tdlh2">(<i>e</i>) Equilibrium of outer layers of the sun.</span><br> +<span class="tdlh2">(<i>f</i>) Observed limit of the Balmer series.</span><br> +<span class="tdlh2">(<i>g</i>) Ionization phenomena.</span></td> +<td></td> +</tr><tr> +<td class="tdl"><span class="allsmcap">IV. THE SOURCE AND COMPOSITION OF THE STELLAR SPECTRUM</span></td> +<td class="tdr"><a href="#Page_46">46</a></td> +</tr><tr> +<td class="tdlh">General appearance of the stellar spectrum.<br> +<span class="tdlh">Descriptive definitions.</span><br> +<span class="tdlh">The continuous background.</span><br> +<span class="tdlh">The reversing layer.</span><br> +<span class="tdlh">Emission lines.</span></td> +<td></td> +</tr><tr> +<td class="tdl"><span class="allsmcap">V. ELEMENTS AND COMPOUNDS IN STELLAR ATMOSPHERES</span></td> +<td class="tdr"><a href="#Page_55">55</a></td> +</tr><tr> +<td class="tdlh">Identifications with laboratory spectra.<br> +<span class="tdlh">Occurrence and behavior of known lines in stellar spectra.</span> +<span class="pagenum" id="Page_viii">[Pg viii]</span></td> +<td></td> +</tr><tr> +<td class="tdc" colspan="2">PART II</td> +</tr><tr> +<td class="tdc" colspan="2">THEORY OF THERMAL IONIZATION</td> +</tr><tr> +<td class="tdl"><span class="allsmcap">VI. THE HIGH-TEMPERATURE ABSORPTION SPECTRUM OF A GAS</span></td> +<td class="tdr"><a href="#Page_91">91</a></td> +</tr><tr> +<td class="tdlh">The schematic reversing layer.<br> +<span class="tdlh">The absorption of radiation.</span><br> +<span class="tdlh">Low temperature conditions.</span><br> +<span class="tdlh">Ultimate lines.</span><br> +<span class="tdlh">Ionization.</span><br> +<span class="tdlh">Production of subordinate lines.</span><br> +<span class="tdlh">Lines of ionized atoms.</span><br> +<span class="tdlh">Summary.</span></td> +<td></td> +</tr><tr> +<td class="tdl"><span class="allsmcap">VII. CRITICAL DISCUSSION OF IONIZATION THEORY</span></td> +<td class="tdr"><a href="#Page_105">105</a></td> +</tr><tr> +<td class="tdlh">Saha’s treatment—marginal appearance.<br> +<span class="tdlh">Theoretical formulae.</span><br> +<span class="tdlh">Physical constants required by the formulae.</span><br> +<span class="tdlh">Assumptions necessary for the application.</span><br> +<span class="tdlh">Laboratory evidence bearing on the theory.</span><br> +<span class="tdlh2">(<i>a</i>) Ultimate lines.</span><br> +<span class="tdlh2">(<i>b</i>) Temperature classes.</span><br> +<span class="tdlh2">(<i>c</i>) Furnace experiments.</span><br> +<span class="tdlh2">(<i>d</i>) Conductivity of flames.</span><br> +<span class="tdlh">Solar intensities as a test of ionization theory.</span></td> +<td></td> +</tr><tr> +<td class="tdl"><span class="allsmcap">VIII. OBSERVATIONAL MATERIAL FOR THE TEST OF IONIZATION +THEORY</span></td> +<td class="tdr"><a href="#Page_116">116</a></td> +</tr><tr> +<td class="tdlh">Measurement of line intensity.<br> +<span class="tdlh">Method of standardization.</span><br> +<span class="tdlh">Summary of results.</span><br> +<span class="tdlh">Consistency of results.</span></td> +<td></td> +</tr><tr> +<td class="tdl"><span class="allsmcap">IX. THE IONIZATION TEMPERATURE SCALE</span></td> +<td class="tdr"><a href="#Page_133">133</a></td> +</tr><tr> +<td class="tdlh">Consistency of the preliminary scale.<br> +<span class="tdlh">Effect of pressure.</span><br> +<span class="tdlh">Levels of origin of ultimate and subordinate lines.</span><br> +<span class="tdlh">Influence of relative abundance.</span><br> +<span class="tdlh">Method of determining effective partial pressure.</span><br> +<span class="tdlh">The corrected temperature scale.</span> +<span class="pagenum" id="Page_ix">[Pg ix]</span></td> +<td></td> +</tr><tr> +<td class="tdl"><span class="allsmcap">X. THE IONIZATION TEMPERATURE SCALE</span></td> +<td class="tdr"><a href="#Page_133">133</a></td> +</tr><tr> +<td class="tdc" colspan="2">PART III</td> +</tr><tr> +<td class="tdc" colspan="2">ADDITIONAL DEDUCTIONS FROM IONIZATION THEORY</td> +</tr><tr> +<td class="tdl"><span class="allsmcap">XI. THE ASTROPHYSICAL EVALUATION OF PHYSICAL CONSTANTS</span></td> +<td class="tdr"><a href="#Page_155">155</a></td> +</tr><tr> +<td class="tdlh">Spectroscopic constants (Plaskett).<br> +<span class="tdlh">Critical potentials (Payne).</span><br> +<span class="tdlh">Duration of atomic states (Milne).</span></td> +<td></td> +</tr><tr> +<td class="tdl"><span class="allsmcap">XII. SPECIAL PROBLEMS IN STELLAR ATMOSPHERES</span></td> +<td class="tdr"><a href="#Page_161">161</a></td> +</tr><tr> +<td class="tdlh">Class \(O\) stars.<br> +<span class="tdlh">Class \(A\) stars.</span><br> +<span class="tdlh2">The Balmer lines.</span><br> +<span class="tdlh2">Classification of \(A\) stars.</span><br> +<span class="tdlh2">Silicon and Strontium stars.</span><br> +<span class="tdlh2">Peculiar Class \(A\) stars.</span><br> +<span class="tdlh">c-stars.</span></td> +<td></td> +</tr><tr> +<td class="tdl"><span class="allsmcap">XIII. THE RELATIVE ABUNDANCE OF THE ELEMENTS</span></td> +<td class="tdr"><a href="#Page_177">177</a></td> +</tr><tr> +<td class="tdlh">Terrestrial data.<br> +<span class="tdlh">Astrophysical data.</span><br> +<span class="tdlh">Uniformity of composition of stellar atmospheres.</span><br> +<span class="tdlh">Marginal appearance.</span><br> +<span class="tdlh">Comparison of stellar and terrestrial estimates.</span></td> +<td></td> +</tr><tr> +<td class="tdl"><span class="allsmcap">XIV. THE MEANING OF STELLAR CLASSIFICATION</span></td> +<td class="tdr"><a href="#Page_190">190</a></td> +</tr><tr> +<td class="tdlh">Principles of classification.<br> +<span class="tdlh">Object of the Draper Classification.</span><br> +<span class="tdlh">Method of classifying.</span><br> +<span class="tdlh">Finer Subdivisions of the Draper Classes.</span><br> +<span class="tdlh">Implications of the Draper system.</span><br> +<span class="tdlh">Homogeneity of the classes.</span><br> +<span class="tdlh">Spectral differences between giants and dwarfs.</span></td> +<td></td> +</tr><tr> +<td class="tdl"><span class="allsmcap">XV. ON THE FUTURE OF THE PROBLEM</span></td> +<td class="tdr"><a href="#Page_199">199</a></td> +</tr><tr> +<td class="tdl">APPENDICES</td> +<td></td> +</tr><tr> +<td class="tdl"><span class="allsmcap">I. INDEX TO DEFINITIONS</span></td> +<td class="tdr"><a href="#Page_203">203</a></td> +</tr><tr> +<td class="tdl"><span class="allsmcap">II. SERIES RELATIONS IN LINE SPECTRA</span></td> +<td class="tdr"><a href="#Page_203">203</a></td> +</tr><tr> +<td class="tdl"><span class="allsmcap">III. LIST OF STARS USED IN CHAPTER VIII</span></td> +<td class="tdr"><a href="#Page_205">205</a></td> +</tr><tr> +<td class="tdl"><span class="allsmcap">IV. INTENSITY CHANGES OF LINES WITH UNKNOWN SERIES +RELATIONS</span></td> +<td class="tdr"><a href="#Page_207">207</a></td> +</tr><tr> +<td class="tdl"><span class="allsmcap">V. MATERIAL ON A STARS, QUOTED IN CHAPTER XII</span></td> +<td class="tdr"><a href="#Page_208">208</a></td> +</tr><tr> +<td class="tdl">SUBJECT INDEX</td> +<td class="tdr"><a href="#Page_211">211</a></td> +</tr><tr> +<td class="tdl">NAME INDEX</td> +<td class="tdr"><a href="#Page_214">214</a></td> +</tr> + </tbody> +</table> + +<hr class="chap x-ebookmaker-drop"> + +<div class="chapter"> +<h2 class="nobreak" id="PART_I">PART I<br> +THE PHYSICAL GROUNDWORK</h2> +</div> + + +<hr class="chap x-ebookmaker-drop"> + +<div class="chapter"> +<p><span class="pagenum" id="Page_3">[Pg 3]</span></p> +<h2 class="nobreak" id="CHAPTER_I">CHAPTER I<br> +THE LABORATORY BASIS OF ASTROPHYSICS</h2> +</div> + +<p class="nind"> +THE application of physics in the domain of astronomy constitutes +a line of investigation that seems to possess almost unbounded +possibilities. In the stars we examine matter in quantities and under +conditions unattainable in the laboratory. The increase in scope is +counterbalanced, however, by a serious limitation—the stars are +not accessible to experiment, only to observation, and there is no +very direct way to establish the validity of laws, deduced in the +laboratory, when they are extrapolated to stellar conditions.</p> + +<p>The verification of physical laws is not, however, the primary object +of the application of physics to the stars. The astrophysicist is +generally obliged to <i>assume</i> their validity in applying them to +stellar conditions. Ultimately it may be that the consistency of the +findings in different branches of astrophysics will form a basis for a +more general verification of physical laws than can be attained in the +laboratory; but at present, terrestrial physics must be the groundwork +of the study of stellar conditions. Hence it is necessary for the +astrophysicist to have ready for application the latest data in every +relevant branch of physical science, realizing which parts of modern +physical theory are still in a tentative stage, and exercising due +caution in applying these to cosmical problems.</p> + +<p>The recent advance of astrophysics has been greatly assisted by the +development, during the last decade, of atomic and radiation theory. +The claim that it would have been possible to predict the existence, +masses, temperatures, and luminosities of the stars from the laws +of radiation, without recourse to stellar observations, represents +the triumph of the theory of radiation. It is equally true that the +main features of the spectra of the stars could be predicted from a +knowledge of atomic structure and the origin of spectra. The theory of +<span class="pagenum" id="Page_4">[Pg 4]</span> +radiation has permitted an analysis of the central conditions of stars, +while atomic theory enables us to analyze the only portion of the star +that can be directly observed—the exceedingly tenuous atmosphere.</p> + +<p>The present book is concerned with the second of these two problems, +the analysis of the superficial layers, and it approaches the +subject of the physical chemistry of stellar atmospheres by treating +terrestrial physics as the basis of cosmical physics. From a brief +working summary of useful physical data (<a href="#CHAPTER_I">Chapter I</a>) and a synopsis of +the conditions under which the application is to be made +(<a href="#CHAPTER_II">Chapters II</a> and <a href="#CHAPTER_III">Chapter III</a>), we shall pass to an analysis of stellar atmospheres by +means of modern spectrum theory. The standpoint adopted is primarily +observational, and new data obtained by the writer in the course of the +investigation will be presented as part of the discussion.</p> + +<p>The first chapter contains a synopsis of the chief data which bear on +atomic structure—the nuclear properties, and the disposition of the +electrons around the nucleus. The origin of line spectra is discussed, +and the ionization potentials corresponding to different atoms are +tabulated. Lastly a brief summary is made of the effect of external +conditions, such as temperature, pressure, and magnetic or electric +fields, upon a line spectrum.</p> + + +<p class="nindc space-above2"> +ATOMIC PROPERTIES ASSOCIATED WITH THE NUCLEUS</p> + + +<p>The properties determined by the atomic nucleus are the mass, and the +isotopic and radioactive properties. The astrophysical study of these +factors is as yet in an elementary stage, but it seems that all three +have a bearing on the frequency of atomic species, and that future +theory may also relate them to the problem of the source and fate of +stellar energy. Moreover, up to the present no general formulation of +the theory of the formation and stability of the elements has been +possible, and it is well to keep in mind the data which are apparently +most relevant to the problem—the observational facts relating to +the nucleus. Probably the study of the nucleus involves the most +fundamental<span class="pagenum" id="Page_5">[Pg 5]</span> +of all cosmical problems—a problem, moreover, which is +largely in the hands of the laboratory physicist.</p> + +<p>The chief nuclear data are summarized in Table I. Successive columns +contain the atomic number, the element and its chemical symbol, the +atomic weight<a id="FNanchor_1" href="#Footnote_1" class="fnanchor">[1]</a> and the mass numbers of the known isotopes,<a id="FNanchor_2" href="#Footnote_2" class="fnanchor">[2]</a> the +percentage terrestrial abundance,<a id="FNanchor_3" href="#Footnote_3" class="fnanchor">[3]</a> expressed in atoms, and the +recorded stellar occurrence. Presence in the stars is indicated by an +asterisk, absence by a dash.</p> + +<h2><a id="TABLE_I">TABLE I</a></h2> + +<table class="autotable"> + <thead><tr> + <th class="tdc bb bt2 br">No.</th> + <th class="tdc bb bt2 br" colspan="2">Element</th> + <th class="tdc bb bt2 br">Atomic<br> + Weight</th> + <th class="tdc bb bt2 br">Isotopes</th> + <th class="tdc bb bt2 br">Percentage<br> + Terrestrial<br> + Abundance<br> + (Atoms)</th> + <th class="tdc bb bt2">Stellar<br> + Occurrences</th> + </tr> + </thead> + <tbody><tr> + <td class="tdl br">1</td> + <td class="tdl">Hydrogen</td> + <td class="tdl br">H</td> + <td class="tdc br">1.008</td> + <td class="tdc br">1.008</td> + <td class="tdc br">15.459</td> + <td class="tdc">*</td> + </tr><tr> + <td class="tdl br">2</td> + <td class="tdl">Helium</td> + <td class="tdl br">He</td> + <td class="tdc br">4.00</td> + <td class="tdc br">4</td> + <td class="tdc br">..</td> + <td class="tdc">*</td> + </tr><tr> + <td class="tdl br">3</td> + <td class="tdl">Lithium</td> + <td class="tdl br">Li</td> + <td class="tdc br">6.94</td> + <td class="tdc br">7, 6</td> + <td class="tdc br">0.0129</td> + <td class="tdc">*</td> + </tr><tr> + <td class="tdl br">4</td> + <td class="tdl">Beryllium</td> + <td class="tdl br">Be</td> + <td class="tdc br">9.01</td> + <td class="tdc br">9</td> + <td class="tdc br">0.0020</td> + <td class="tdc">—</td> + </tr><tr> + <td class="tdl br">5</td> + <td class="tdl">Boron</td> + <td class="tdl br">B</td> + <td class="tdc br">11.0</td> + <td class="tdc br">11, 10</td> + <td class="tdc br">0.0016</td> + <td class="tdc">—</td> + </tr><tr> + <td class="tdl br">6</td> + <td class="tdl">Carbon</td> + <td class="tdl br">C</td> + <td class="tdc br">12.005</td> + <td class="tdc br">12</td> + <td class="tdc br">0.2069</td> + <td class="tdc">*</td> + </tr><tr> + <td class="tdl br">7</td> + <td class="tdl">Nitrogen</td> + <td class="tdl br">N</td> + <td class="tdc br">14.01</td> + <td class="tdc br">14</td> + <td class="tdc br">0.0383</td> + <td class="tdc">*</td> + </tr><tr> + <td class="tdl br">8</td> + <td class="tdl">Oxygen</td> + <td class="tdl br">O</td> + <td class="tdc br">16.00</td> + <td class="tdc br">16</td> + <td class="tdc br">59.940</td> + <td class="tdc">*</td> + </tr><tr> + <td class="tdl br">9</td> + <td class="tdl">Fluorine</td> + <td class="tdl br">F</td> + <td class="tdc br">19.0</td> + <td class="tdc br">19</td> + <td class="tdc br">0.0282</td> + <td class="tdc">—</td> + </tr><tr> + <td class="tdl br">10</td> + <td class="tdl">Neon</td> + <td class="tdl br">Ne</td> + <td class="tdc br">20.0</td> + <td class="tdc br">20, 22, (21)</td> + <td class="tdc br">..</td> + <td class="tdc">—</td> + </tr><tr> + <td class="tdl br">11</td> + <td class="tdl">Sodium</td> + <td class="tdl br">Na</td> + <td class="tdc br">23.00</td> + <td class="tdc br">23</td> + <td class="tdc br">2.028</td> + <td class="tdc">*</td> + </tr><tr> + <td class="tdl br">12</td> + <td class="tdl">Magnesium</td> + <td class="tdl br">Mg</td> + <td class="tdc br">24.32</td> + <td class="tdc br">24, 25, 26</td> + <td class="tdc br">1.426</td> + <td class="tdc">*</td> + </tr><tr> + <td class="tdl br">13</td> + <td class="tdl">Aluminium</td> + <td class="tdl br">Al</td> + <td class="tdc br">27.1</td> + <td class="tdc br"></td> + <td class="tdc br">4.946</td> + <td class="tdc">*</td> + </tr><tr> + <td class="tdl br">14</td> + <td class="tdl">Silicon</td> + <td class="tdl br">Si</td> + <td class="tdc br">28.3</td> + <td class="tdc br">28, 29, 30</td> + <td class="tdc br">16.235</td> + <td class="tdc">*</td> + </tr><tr> + <td class="tdl br">15</td> + <td class="tdl">Phosphorus</td> + <td class="tdl br">P</td> + <td class="tdc br">31.04</td> + <td class="tdc br">31</td> + <td class="tdc br">0.0818</td> + <td class="tdc">—</td> + </tr><tr> + <td class="tdl br">16</td> + <td class="tdl">Sulphur</td> + <td class="tdl br">S</td> + <td class="tdc br">32.06</td> + <td class="tdc br">32</td> + <td class="tdc br">0.0518</td> + <td class="tdc">*</td> + </tr><tr> + <td class="tdl br">17</td> + <td class="tdl">Chlorine</td> + <td class="tdl br">Cl</td> + <td class="tdc br">35.46</td> + <td class="tdc br">35, 37, (39)</td> + <td class="tdc br">0.1149</td> + <td class="tdc">—</td> + </tr><tr> + <td class="tdl br">18</td> + <td class="tdl">Argon</td> + <td class="tdl br">A</td> + <td class="tdc br">39.88</td> + <td class="tdc br">40, 36</td> + <td class="tdc br">..</td> + <td class="tdc">—</td> + </tr><tr> + <td class="tdl br">19</td> + <td class="tdl">Potassium</td> + <td class="tdl br">K</td> + <td class="tdc br">39.10</td> + <td class="tdc br">39, 41</td> + <td class="tdc br">1.088</td> + <td class="tdc">*</td> + </tr><tr> + <td class="tdl br">20</td> + <td class="tdl">Calcium</td> + <td class="tdl br">Ca</td> + <td class="tdc br">40.07</td> + <td class="tdc br">(40, 44)</td> + <td class="tdc br">1.503</td> + <td class="tdc">*</td> + </tr><tr> + <td class="tdl br">21</td> + <td class="tdl">Scandium</td> + <td class="tdl br">Sc</td> + <td class="tdc br">44.1</td> + <td class="tdc br">45</td> + <td class="tdc br">..</td> + <td class="tdc">*</td> + </tr><tr> + <td class="tdl br">22</td> + <td class="tdl">Titanium</td> + <td class="tdl br">Ti</td> + <td class="tdc br">48.1</td> + <td class="tdc br">48</td> + <td class="tdc br">0.2407</td> + <td class="tdc">*</td> + </tr><tr> + <td class="tdl br">23</td> + <td class="tdl">Vanadium</td> + <td class="tdl br">V</td> + <td class="tdc br">51.0</td> + <td class="tdc br">51</td> + <td class="tdc br">0.0133</td> + <td class="tdc">* +<span class="pagenum" id="Page_6">[Pg 6]</span></td> +</tr><tr> +<td class="tdl br">24</td> + <td class="tdl">Chromium</td> + <td class="tdl br">Cr</td> + <td class="tdc br">52.0</td> + <td class="tdc br">52</td> + <td class="tdc br">0.0213</td> + <td class="tdc">*</td> + </tr><tr> + <td class="tdl br">25</td> + <td class="tdl">Manganese</td> + <td class="tdl br">Mn</td> + <td class="tdc br">54.93</td> + <td class="tdc br">55</td> + <td class="tdc br">0.0351</td> + <td class="tdc">*</td> + </tr><tr> + <td class="tdl br">26</td> + <td class="tdl">Iron</td> + <td class="tdl br">Fe</td> + <td class="tdc br">55.84</td> + <td class="tdc br">54, 56</td> + <td class="tdc br">1.485</td> + <td class="tdc">*</td> + </tr><tr> + <td class="tdl br">27</td> + <td class="tdl">Cobalt</td> + <td class="tdl br">Co</td> + <td class="tdc br">58.97</td> + <td class="tdc br">59</td> + <td class="tdc br">0.0009</td> + <td class="tdc">*</td> + </tr><tr> + <td class="tdl br">28</td> + <td class="tdl">Nickel</td> + <td class="tdl br">Ni</td> + <td class="tdc br">58.68</td> + <td class="tdc br">58, 60</td> + <td class="tdc br">0.0091</td> + <td class="tdc">*</td> + </tr><tr> + <td class="tdl br">29</td> + <td class="tdl">Copper</td> + <td class="tdl br">Cu</td> + <td class="tdc br">63.57</td> + <td class="tdc br">63, 65</td> + <td class="tdc br">0.0028</td> + <td class="tdc">*</td> + </tr><tr> + <td class="tdl br">30</td> + <td class="tdl">Zinc</td> + <td class="tdl br">Zn</td> + <td class="tdc br">65.37</td> + <td class="tdc br">(64, 66, 68, 70)</td> + <td class="tdc br">0.0011</td> + <td class="tdc">*</td> + </tr><tr> + <td class="tdl br">31</td> + <td class="tdl">Gallium</td> + <td class="tdl br">Ga</td> + <td class="tdc br">69.9</td> + <td class="tdc br">69, 71</td> + <td class="tdc br">..</td> + <td class="tdc">—</td> + </tr><tr> + <td class="tdl br">32</td> + <td class="tdl">Germanium</td> + <td class="tdl br">Ge</td> + <td class="tdc br">72.5</td> + <td class="tdc br">74, 72, 70</td> + <td class="tdc br">..</td> + <td class="tdc">—</td> + </tr><tr> + <td class="tdl br">33</td> + <td class="tdl">Arsenic</td> + <td class="tdl br">As</td> + <td class="tdc br">74.96</td> + <td class="tdc br">75</td> + <td class="tdc br">..</td> + <td class="tdc">—</td> + </tr><tr> + <td class="tdl br">34</td> + <td class="tdl">Selenium</td> + <td class="tdl br">Se</td> + <td class="tdc br">79.2</td> + <td class="tdc br"></td> + <td class="tdc br">..</td> + <td class="tdc">—</td> + </tr><tr> + <td class="tdl br">35</td> + <td class="tdl">Bromine</td> + <td class="tdl br">Br</td> + <td class="tdc br">79.92</td> + <td class="tdc br">79, 81</td> + <td class="tdc br">..</td> + <td class="tdc">—</td> + </tr><tr> + <td class="tdl_top br">36</td> + <td class="tdl_top">Krypton</td> + <td class="tdl_top br">Kr</td> + <td class="tdc_top br">82.92</td> + <td class="tdc_top br">84, 86, 82, 83, 70,<br> + 78</td> + <td class="tdc_top br">..</td> + <td class="tdc_top">—</td> + </tr><tr> + <td class="tdl br">37</td> + <td class="tdl">Rubidium</td> + <td class="tdl br">Rb</td> + <td class="tdc br">85.45</td> + <td class="tdc br">85, 87</td> + <td class="tdc br">..</td> + <td class="tdc">*</td> + </tr><tr> + <td class="tdl br">38</td> + <td class="tdl">Strontium</td> + <td class="tdl br">Sr</td> + <td class="tdc br">87.63</td> + <td class="tdc br">88, 86</td> + <td class="tdc br">0.0065</td> + <td class="tdc">*</td> + </tr><tr> + <td class="tdl_top br">39</td> + <td class="tdl_top">Yttrium</td> + <td class="tdl_top br">Y</td> + <td class="tdc_top br">88.7</td> + <td class="tdc_top br">89</td> + <td class="tdc_top br">0.0030<br> + (with Ce)</td> + <td class="tdc_top">*</td> + </tr><tr> + <td class="tdl br">40</td> + <td class="tdl">Zirconium</td> + <td class="tdl br">Z</td> + <td class="tdc br">90.6</td> + <td class="tdc br">90, 92, 94</td> + <td class="tdc br">0.0095</td> + <td class="tdc">*</td> + </tr><tr> + <td class="tdl br">41</td> + <td class="tdl">Niobium</td> + <td class="tdl br">Nb</td> + <td class="tdc br">93.1</td> + <td class="tdc br"></td> + <td class="tdc br">..</td> + <td class="tdc">?</td> + </tr><tr> + <td class="tdl br">42</td> + <td class="tdl">Molybdenum</td> + <td class="tdl br">Mo</td> + <td class="tdc br">96</td> + <td class="tdc br"></td> + <td class="tdc br">..</td> + <td class="tdc">*</td> + </tr><tr> + <td class="tdl br">43</td> + <td class="tdl">..</td> + <td class="tdl br"></td> + <td class="tdc br"></td> + <td class="tdc br"></td> + <td class="tdc br">..</td> + <td class="tdc">..</td> + </tr><tr> + <td class="tdl br">44</td> + <td class="tdl">Ruthenium</td> + <td class="tdl br">Ru</td> + <td class="tdc br">101.7</td> + <td class="tdc br"></td> + <td class="tdc br">..</td> + <td class="tdc">*</td> + </tr><tr> + <td class="tdl br">45</td> + <td class="tdl">Rhodium</td> + <td class="tdl br">Rh</td> + <td class="tdc br">102.9</td> + <td class="tdc br"></td> + <td class="tdc br">..</td> + <td class="tdc">*</td> + </tr><tr> + <td class="tdl br">46</td> + <td class="tdl">Palladium</td> + <td class="tdl br">Pd</td> + <td class="tdc br">106.7</td> + <td class="tdc br"></td> + <td class="tdc br">..</td> + <td class="tdc">*</td> + </tr><tr> + <td class="tdl br">47</td> + <td class="tdl">Silver</td> + <td class="tdl br">Ag</td> + <td class="tdc br">107.88</td> + <td class="tdc br">107, 109</td> + <td class="tdc br">..</td> + <td class="tdc">*</td> + </tr><tr> + <td class="tdl_top br">48</td> + <td class="tdl_top">Cadmium</td> + <td class="tdl_top br">Cd</td> + <td class="tdc_top br">112.40</td> + <td class="tdc_top br">110, 111, 112,<br> + 113, 114, 116</td> + <td class="tdc_top br">..</td> + <td class="tdc_top">—</td> + </tr><tr> + <td class="tdl br">49</td> + <td class="tdl">Indium</td> + <td class="tdl br">In</td> + <td class="tdc br">114.8</td> + <td class="tdc br"></td> + <td class="tdc br">..</td> + <td class="tdc">—</td> + </tr><tr> + <td class="tdl br">50</td> + <td class="tdl">Tin</td> + <td class="tdl br">Sn</td> + <td class="tdc br">118.7</td> + <td class="tdc br"></td> + <td class="tdc br">..</td> + <td class="tdc">?</td> + </tr><tr> + <td class="tdl br">51</td> + <td class="tdl">Antimony</td> + <td class="tdl br">Sb</td> + <td class="tdc br">120.2</td> + <td class="tdc br"></td> + <td class="tdc br">..</td> + <td class="tdc">—</td> + </tr><tr> + <td class="tdl br">52</td> + <td class="tdl">Tellurium</td> + <td class="tdl br">Te</td> + <td class="tdc br">127.5</td> + <td class="tdc br">126, 128, 130</td> + <td class="tdc br">..</td> + <td class="tdc">—</td> + </tr><tr> + <td class="tdl br">53</td> + <td class="tdl">Iodine</td> + <td class="tdl br">I</td> + <td class="tdc br">126.92</td> + <td class="tdc br">127</td> + <td class="tdc br">..</td> + <td class="tdc">—</td> + </tr><tr> + <td class="tdl_top br">54</td> + <td class="tdl_top">Xenon</td> + <td class="tdl_top br">Xe</td> + <td class="tdc_top br">130.2</td> + <td class="tdc_top br">129, 132, 131, 134,<br> + 136, (128, 130)</td> + <td class="tdc_top br">..</td> + <td class="tdc_top">—</td> + </tr><tr> + <td class="tdl br">55</td> + <td class="tdl">Caesium</td> + <td class="tdl br">Cs</td> + <td class="tdc br">132.81</td> + <td class="tdc br">133</td> + <td class="tdc br">..</td> + <td class="tdc">*</td> + </tr><tr> + <td class="tdl br">56</td> + <td class="tdl">Barium</td> + <td class="tdl br">Ba</td> + <td class="tdc br">137.37</td> + <td class="tdc br">138</td> + <td class="tdc br">0.0098</td> + <td class="tdc">*</td> + </tr><tr> + <td class="tdl br">57</td> + <td class="tdl">Lanthanum</td> + <td class="tdl br">La</td> + <td class="tdc br">139.0</td> + <td class="tdc br">139</td> + <td class="tdc br">..</td> + <td class="tdc">*</td> + </tr><tr> + <td class="tdl_top br">58</td> + <td class="tdl_top">Cerium</td> + <td class="tdl_top br">Ce</td> + <td class="tdc_top br">140.25</td> + <td class="tdc_top br">140, 142</td> + <td class="tdc_top br">0.0030<br> + (with Y)</td> + <td class="tdc_ws2">*</td> + </tr><tr> + <td class="tdl br">59</td> + <td class="tdl">Praseodymium</td> + <td class="tdl br">Pr</td> + <td class="tdc br">140.9</td> + <td class="tdc br">141</td> + <td class="tdc br">..</td> + <td class="tdc">—<span class="pagenum" id="Page_7">[Pg 7]</span></td> + </tr><tr> +<td class="tdl br">60</td> + <td class="tdl">Neodymium</td> + <td class="tdl br">Nd</td> + <td class="tdc br">144.3</td> + <td class="tdc br">142-150</td> + <td class="tdc br">..</td> + <td class="tdc">—</td> + </tr><tr> + <td class="tdl br">61</td> + <td class="tdl">..</td> + <td class="tdl br"></td> + <td class="tdc br">..</td> + <td class="tdc br"></td> + <td class="tdc br">..</td> + <td class="tdc">..</td> + </tr><tr> + <td class="tdl br">62</td> + <td class="tdl">Samarium</td> + <td class="tdl br">Sa</td> + <td class="tdc br">150.4</td> + <td class="tdc br"></td> + <td class="tdc br">..</td> + <td class="tdc">—</td> + </tr><tr> + <td class="tdl br">63</td> + <td class="tdl">Europium</td> + <td class="tdl br">Eu</td> + <td class="tdc br">152.0</td> + <td class="tdc br"></td> + <td class="tdc br">..</td> + <td class="tdc">*</td> + </tr><tr> + <td class="tdl br">64</td> + <td class="tdl">Gadolinium</td> + <td class="tdl br">Gd</td> + <td class="tdc br">157.3</td> + <td class="tdc br"></td> + <td class="tdc br">..</td> + <td class="tdc">—</td> + </tr><tr> + <td class="tdl br">65</td> + <td class="tdl">Terbium</td> + <td class="tdl br">Tb</td> + <td class="tdc br">159.2</td> + <td class="tdc br"></td> + <td class="tdc br">..</td> + <td class="tdc">*</td> + </tr><tr> + <td class="tdl br">66</td> + <td class="tdl">Dysprosium</td> + <td class="tdl br">Dy</td> + <td class="tdc br">162.5</td> + <td class="tdc br"></td> + <td class="tdc br">..</td> + <td class="tdc">—</td> + </tr><tr> + <td class="tdl br">67</td> + <td class="tdl">Holmium</td> + <td class="tdl br">Ho</td> + <td class="tdc br">163.5</td> + <td class="tdc br"></td> + <td class="tdc br">..</td> + <td class="tdc">—</td> + </tr><tr> + <td class="tdl br">68</td> + <td class="tdl">Erbium</td> + <td class="tdl br">Er</td> + <td class="tdc br">167.7</td> + <td class="tdc br"></td> + <td class="tdc br">..</td> + <td class="tdc">—</td> + </tr><tr> + <td class="tdl br">69</td> + <td class="tdl">Thulium</td> + <td class="tdl br">Tm</td> + <td class="tdc br">168.5</td> + <td class="tdc br"></td> + <td class="tdc br">..</td> + <td class="tdc">—</td> + </tr><tr> + <td class="tdl br">70</td> + <td class="tdl">Ytterbium</td> + <td class="tdl br">Yb</td> + <td class="tdc br">173.5</td> + <td class="tdc br"></td> + <td class="tdc br">..</td> + <td class="tdc">—</td> + </tr><tr> + <td class="tdl br">71</td> + <td class="tdl">Lutecium</td> + <td class="tdl br">Lu</td> + <td class="tdc br">175.0</td> + <td class="tdc br"></td> + <td class="tdc br">..</td> + <td class="tdc">—</td> + </tr><tr> + <td class="tdl br">72</td> + <td class="tdl">Hafnium</td> + <td class="tdl br">Hf</td> + <td class="tdc br"></td> + <td class="tdc br"></td> + <td class="tdc br">..</td> + <td class="tdc">—</td> + </tr><tr> + <td class="tdl br">73</td> + <td class="tdl">Tantalum</td> + <td class="tdl br">Ta</td> + <td class="tdc br">181.5</td> + <td class="tdc br"></td> + <td class="tdc br">..</td> + <td class="tdc">—</td> + </tr><tr> + <td class="tdl br">74</td> + <td class="tdl">Tungsten</td> + <td class="tdl br">W</td> + <td class="tdc br">184.0</td> + <td class="tdc br"></td> + <td class="tdc br">..</td> + <td class="tdc">—</td> + </tr><tr> + <td class="tdl br">75</td> + <td class="tdl">..</td> + <td class="tdl br"></td> + <td class="tdl br"></td> + <td class="tdc br"></td> + <td class="tdc br">..</td> + <td class="tdc">—</td> + </tr><tr> + <td class="tdl br">76</td> + <td class="tdl">Osmium</td> + <td class="tdl br">Os</td> + <td class="tdc br">190.9</td> + <td class="tdc br"></td> + <td class="tdc br">..</td> + <td class="tdc">—</td> + </tr><tr> + <td class="tdl br">77</td> + <td class="tdl">Iridium</td> + <td class="tdl br">Ir</td> + <td class="tdc br">193.1</td> + <td class="tdc br"></td> + <td class="tdc br">..</td> + <td class="tdc">—</td> + </tr><tr> + <td class="tdl br">78</td> + <td class="tdl">Platinum</td> + <td class="tdl br">Pt</td> + <td class="tdc br">195.2</td> + <td class="tdc br"></td> + <td class="tdc br">..</td> + <td class="tdc">—</td> + </tr><tr> + <td class="tdl br">79</td> + <td class="tdl">Gold</td> + <td class="tdl br">Au</td> + <td class="tdc br">197.2</td> + <td class="tdc br"></td> + <td class="tdc br">..</td> + <td class="tdc">—</td> + </tr><tr> + <td class="tdl_top br">80</td> + <td class="tdl_top">Mercury</td> + <td class="tdl_top br">Hg</td> + <td class="tdc_top br">200.6</td> + <td class="tdc_top br">(197, 198, 199,<br> + 200) 202, 204</td> + <td class="tdc_top br">..</td> + <td class="tdc_top">—</td> + </tr><tr> + <td class="tdl br">81</td> + <td class="tdl">Thallium</td> + <td class="tdl br">Tl</td> + <td class="tdc br">204.0</td> + <td class="tdc br"></td> + <td class="tdc br">..</td> + <td class="tdc">—</td> + </tr><tr> + <td class="tdl br">82</td> + <td class="tdl">Lead</td> + <td class="tdl br">Pb</td> + <td class="tdc br">207.2</td> + <td class="tdc br"></td> + <td class="tdc br">0.0002</td> + <td class="tdc">*</td> + </tr><tr> + <td class="tdl br">83</td> + <td class="tdl">Bismuth</td> + <td class="tdl br">Bi</td> + <td class="tdc br">208.0</td> + <td class="tdc br"></td> + <td class="tdc br">..</td> + <td class="tdc">—</td> + </tr><tr> + <td class="tdl br">84</td> + <td class="tdl">..</td> + <td class="tdl br"></td> + <td class="tdl br">..</td> + <td class="tdc br"></td> + <td class="tdc br">..</td> + <td class="tdc">..</td> + </tr><tr> + <td class="tdl br">85</td> + <td class="tdl">..</td> + <td class="tdl br"></td> + <td class="tdc br">..</td> + <td class="tdc br"></td> + <td class="tdc br">..</td> + <td class="tdc">..</td> + </tr><tr> + <td class="tdl br">86</td> + <td class="tdl">Radon</td> + <td class="tdl br">Rd</td> + <td class="tdc br">222.4</td> + <td class="tdc br"></td> + <td class="tdc br">..</td> + <td class="tdc">—</td> + </tr><tr> + <td class="tdl br">87</td> + <td class="tdl">..</td> + <td class="tdl br"></td> + <td class="tdc br">..</td> + <td class="tdc br"></td> + <td class="tdc br">..</td> + <td class="tdc">..</td> + </tr><tr> + <td class="tdl br">88</td> + <td class="tdl">Radium</td> + <td class="tdl br">Ra</td> + <td class="tdc br">226.0</td> + <td class="tdc br"></td> + <td class="tdc br">..</td> + <td class="tdc">—</td> + </tr><tr> + <td class="tdl br">89</td> + <td class="tdl">..</td> + <td class="tdl br"></td> + <td class="tdl br">..</td> + <td class="tdc br"></td> + <td class="tdc br">..</td> + <td class="tdc">..</td> + </tr><tr> + <td class="tdl br">90</td> + <td class="tdl">Thorium</td> + <td class="tdl br">Th</td> + <td class="tdc br">232.4</td> + <td class="tdl br"></td> + <td class="tdc br">..</td> + <td class="tdc">—</td> + </tr><tr> + <td class="tdl br">91</td> + <td class="tdl">..</td> + <td class="tdl br"></td> + <td class="tdl br">..</td> + <td class="tdc br"></td> + <td class="tdc br">..</td> + <td class="tdc">..</td> + </tr><tr> + <td class="tdl bb br">92</td> + <td class="tdl bb">Uranium</td> + <td class="tdl bb br">U</td> + <td class="tdc bb br">238.2</td> + <td class="tdc bb br"></td> + <td class="tdc bb br">..</td> + <td class="tdc bb"><span class="pagenum" id="Page_8">[Pg 8]</span>—</td> + </tr> + </tbody> +</table> + + +<p class="nindc space-above2"> +ARRANGEMENT OF EXTRA-NUCLEAR ELECTRONS</p> + + +<p>Logically a description of the analysis of spectra should precede +the discussion of electron arrangement, for our knowledge of the +extra-nuclear electrons is very largely based on spectroscopic +evidence. The established conceptions of atomic structure, however, +are useful in classifying mentally the general outlines of the origin +of line spectra, and therefore, for convenience of reference, Bohr’s +table<a id="FNanchor_4" href="#Footnote_4" class="fnanchor">[4]</a> of the arrangement of extra-nuclear electrons is here prefixed +to our brief discussion of spectroscopic data. The chemical elements +are given in order of atomic number, and successive columns contain, +for the atom in its normal state, the numbers of electrons in the +various quantum orbits.</p> + +<figure class="figcenter" id="i001"> +<img src="images/i001.jpg" width="2000" height="941" alt="i001"> +<figcaption class="caption"> + +<p>Figure 1</p> + +<p>Arrangement of electron orbits for the atom of neutral sodium. +Orbits consisting partly of broken lines are circular orbits seen in +perspective. The numbers and quantum relations of the orbits are as +follows: inner shell, two \(1_2\) orbits; next shell, four \(2_2\) +orbits and four \(2_1\) orbits; outer electron \(3_1\) orbit.</p></figcaption> +</figure> + +<p>In accordance with the notation of Bohr and Kramers,<a id="FNanchor_5" href="#Footnote_5" class="fnanchor">[5]</a> the first +figure in the orbit-designation that stands at the head of a column +denotes the total quantum number, which determines the length of the +major axis of the corresponding orbit. The subscript is the so-called +azimuthal quantum number, which determines the ellipticity of the +orbit; the orbits with the smallest azimuthal quantum numbers are the +most eccentric, and those for which the azimuthal quantum number is +<span class="pagenum" id="Page_9">[Pg 9]</span> +equal to the total quantum number are circular. The diagram (<a href="#i001">Figure 1</a>) +represents the normal arrangement of electrons around the nucleus of +the sodium atom, which possesses eleven extra-nuclear electrons.</p> + +<h2><a id="TABLE_II">TABLE II</a></h2> + +<table class="autotable"> +<thead><tr> +<th class="tdc bb bt2 br">No.</th> +<th class="tdc bb bt2 br"> Elt. </th> +<th class="tdc bb bt2 br"> 1₁ </th> +<th class="tdc bb bt2"> 2₁ </th> +<th class="tdc bb bt2 br"> 2₂ </th> +<th class="tdc bb bt2"> 3₁ </th> +<th class="tdc bb bt2"> 3₂ </th> +<th class="tdc bb bt2 br"> 3₃ </th> +<th class="tdc bb bt2"> 4₁ </th> +<th class="tdc bb bt2"> 4₂ </th> +<th class="tdc bb bt2"> 4₃ </th> +<th class="tdc bb bt2 br"> 4₄ </th> +<th class="tdc bb bt2"> 5₁ </th> +<th class="tdc bb bt2"> 5₂ </th> +<th class="tdc bb bt2"> 5₃ </th> +<th class="tdc bb bt2"> 5₄ </th> +<th class="tdc bb bt2 br"> 5₅ </th> +<th class="tdc bb bt2"> 6₁ </th> +<th class="tdc bb bt2"> 6₂ </th> +<th class="tdc bb bt2"> 6₃ </th> +<th class="tdc bb bt2"> 6₄ </th> +<th class="tdc bb bt2"> 6₅ </th> +<th class="tdc bb bt2 br"> 6₆ </th> +<th class="tdc bb bt2"> 7₁ </th> +<th class="tdc bb bt2"> 7₂ </th> +</tr> +</thead> +<tbody><tr> +<td class="tdl br">1</td> +<td class="tdl_ws1 br">H</td> +<td class="tdc br">1</td> +<td class="tdc"> </td> +<td class="tdc br"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc br"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc br"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc br"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc br"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +</tr><tr> +<td class="tdl br">2</td> +<td class="tdl_ws1 br">He</td> +<td class="tdc br">2</td> +<td class="tdc"> </td> +<td class="tdc br"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc br"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc br"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc br"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc br"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +</tr><tr> +<td class="tdl br">3</td> +<td class="tdl_ws1 br">Li</td> +<td class="tdc br">2</td> +<td class="tdc">1</td> +<td class="tdc br"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc br"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc br"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc br"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc br"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +</tr><tr> +<td class="tdl br">4</td> +<td class="tdl_ws1 br">Be</td> +<td class="tdc br">2</td> +<td class="tdc">2</td> +<td class="tdc br"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc br"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc br"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc br"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc br"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +</tr><tr> +<td class="tdl br">5</td> +<td class="tdl_ws1 br">B</td> +<td class="tdc br">2</td> +<td class="tdc">2</td> +<td class="tdc br">(1)</td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc br"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc br"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc br"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc br"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +</tr><tr> +<td class="tdl br">6</td> +<td class="tdl_ws1 br">C</td> +<td class="tdc br">2</td> +<td class="tdc">2</td> +<td class="tdc br">2</td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc br"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc br"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc br"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc br"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +</tr><tr> +<td class="tdl br">7</td> +<td class="tdl_ws1 br">N</td> +<td class="tdc br">2</td> +<td class="tdc">4</td> +<td class="tdc br">1</td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc br"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc br"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc br"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc br"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +</tr><tr> +<td class="tdl br">8</td> +<td class="tdl_ws1 br">O</td> +<td class="tdc br">2</td> +<td class="tdc">4</td> +<td class="tdc br">2</td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc br"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc br"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc br"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc br"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +</tr><tr> +<td class="tdl br">9</td> +<td class="tdl_ws1 br">F</td> +<td class="tdc br">2</td> +<td class="tdc">4</td> +<td class="tdc br">3</td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc br"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc br"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc br"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc br"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +</tr><tr> +<td class="tdl br">10</td> +<td class="tdl_ws1 br">Ne</td> +<td class="tdc br">2</td> +<td class="tdc">4</td> +<td class="tdc br">4</td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc br"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc br"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc br"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc br"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +</tr><tr> +<td class="tdl br">11</td> +<td class="tdl_ws1 br">Na</td> +<td class="tdc br">2</td> +<td class="tdc">4</td> +<td class="tdc br">4</td> +<td class="tdc">1</td> +<td class="tdc"> </td> +<td class="tdc br"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc br"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> 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br">4</td> +<td class="tdc">2</td> +<td class="tdc">1</td> +<td class="tdc br"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc br"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc br"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc br"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +</tr><tr> +<td class="tdl br">14</td> +<td class="tdl_ws1 br">Si</td> +<td class="tdc br">2</td> +<td class="tdc">4</td> +<td class="tdc br">4</td> +<td class="tdc">(2)</td> +<td class="tdc">(2)</td> +<td class="tdc br"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc br"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc br"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> 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class="tdc">6</td> +<td class="tdc br">6</td> +<td class="tdc">8</td> +<td class="tdc">8</td> +<td class="tdc">8</td> +<td class="tdc br">8</td> +<td class="tdc">6</td> +<td class="tdc">6</td> +<td class="tdc">6</td> +<td class="tdc">-</td> +<td class="tdc br">-</td> +<td class="tdc">4</td> +<td class="tdc">1</td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc br"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdl_ws1 br"></td> +<td class="tdc br"></td> +<td class="tdc"></td> +<td class="tdc br"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc br"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc br"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc br"></td> +<td class="tdc"></td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc br"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +</tr><tr> +<td class="tdl br">86</td> +<td class="tdl_ws1 br">Rd</td> +<td class="tdc br">2</td> +<td class="tdc">4</td> +<td class="tdc br">4</td> +<td class="tdc">6</td> +<td class="tdc">6</td> +<td class="tdc br">6</td> +<td class="tdc">8</td> +<td class="tdc">8</td> +<td class="tdc">8</td> +<td class="tdc br">8</td> +<td class="tdc">6</td> +<td class="tdc">6</td> +<td class="tdc">6</td> +<td class="tdc">-</td> +<td class="tdc br">-</td> +<td class="tdc">4</td> +<td class="tdc">4</td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc br"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdl_ws1 br"></td> +<td class="tdc br"></td> +<td class="tdc"></td> +<td class="tdc br"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc br"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc br"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc br"></td> +<td class="tdc"></td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc br"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +</tr><tr> +<td class="tdl br">88</td> +<td class="tdl_ws1 br">Ra</td> +<td class="tdc br">2</td> +<td class="tdc">4</td> +<td class="tdc br">4</td> +<td class="tdc">6</td> +<td class="tdc">6</td> +<td class="tdc br">6</td> +<td class="tdc">8</td> +<td class="tdc">8</td> +<td class="tdc">8</td> +<td class="tdc br">8</td> +<td class="tdc">6</td> +<td class="tdc">6</td> +<td class="tdc">6</td> +<td class="tdc">-</td> +<td class="tdc br">-</td> +<td class="tdc">4</td> +<td class="tdc">4</td> +<td class="tdc">-</td> +<td class="tdc">-</td> +<td class="tdc">-</td> +<td class="tdc br">-</td> +<td class="tdc">2</td> +<td class="tdc"> </td> +</tr><tr> +<td class="tdl br">89</td> +<td class="tdl_ws1 br">Ac</td> +<td class="tdc br">2</td> +<td class="tdc">4</td> +<td class="tdc br">4</td> +<td class="tdc">6</td> +<td class="tdc">6</td> +<td class="tdc br">6</td> +<td class="tdc">8</td> +<td class="tdc">8</td> +<td class="tdc">8</td> +<td class="tdc br">8</td> +<td class="tdc">6</td> +<td class="tdc">6</td> +<td class="tdc">6</td> +<td class="tdc">-</td> +<td class="tdc br">-</td> +<td class="tdc">4</td> +<td class="tdc">4</td> +<td class="tdc">1</td> +<td class="tdc">-</td> +<td class="tdc">-</td> +<td class="tdc br">-</td> +<td class="tdc">(2)</td> +<td class="tdc"> </td> +</tr><tr> +<td class="tdl br">90</td> +<td class="tdl_ws1 br">Th</td> +<td class="tdc br">2</td> +<td class="tdc">4</td> +<td class="tdc br">4</td> +<td class="tdc">6</td> +<td class="tdc">6</td> +<td class="tdc br">6</td> +<td class="tdc">8</td> +<td class="tdc">8</td> +<td class="tdc">8</td> +<td class="tdc br">8</td> +<td class="tdc">6</td> +<td class="tdc">6</td> +<td class="tdc">6</td> +<td class="tdc">-</td> +<td class="tdc br">-</td> +<td class="tdc">4</td> +<td class="tdc">4</td> +<td class="tdc">2</td> +<td class="tdc">-</td> +<td class="tdc">-</td> +<td class="tdc br">-</td> +<td class="tdc">(2)</td> +<td class="tdc"> </td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdl_ws1 br"></td> +<td class="tdc br"></td> +<td class="tdc"></td> +<td class="tdc br"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc br"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc br"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc br"></td> +<td class="tdc"></td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +<td class="tdc br"> </td> +<td class="tdc"> </td> +<td class="tdc"> </td> +</tr><tr> +<td class="tdl br bb">118</td> +<td class="tdl_ws1 br bb">?</td> +<td class="tdc br bb">2</td> +<td class="tdc bb">4</td> +<td class="tdc br bb">4</td> +<td class="tdc bb">6</td> +<td class="tdc bb">6</td> +<td class="tdc br bb">6</td> +<td class="tdc bb">8</td> +<td class="tdc bb">8</td> +<td class="tdc bb">8</td> +<td class="tdc br bb">8</td> +<td class="tdc bb">8</td> +<td class="tdc bb">8</td> +<td class="tdc bb">8</td> +<td class="tdc bb">8</td> +<td class="tdc br bb">-</td> +<td class="tdc bb">6</td> +<td class="tdc bb">6</td> +<td class="tdc bb">6</td> +<td class="tdc bb">-</td> +<td class="tdc bb">-</td> +<td class="tdc br bb">-</td> +<td class="tdc bb">4</td> +<td class="tdc bb">4</td> +</tr> +</tbody> +</table> + + +<p>The table also gives the number of spectroscopic valency electrons, +a quantity which is required by the theory of thermal ionization. +The spectroscopic valency electrons are those in <i>equivalent outer +orbits</i> (outer orbits of equal total quantum number which have the +same azimuthal quantum number). The number is not necessarily the same +as the number of chemical valencies (the number of orbits with the same +<i>total</i> quantum number) although the two values coincide for the +alkali metals and for the alkaline earths. For carbon,<a id="FNanchor_6" href="#Footnote_6" class="fnanchor">[6]</a> on the other +<span class="pagenum" id="Page_11">[Pg 11]</span> +hand, the number of spectroscopic valency electrons is two (the number +of 22 orbits), while the chemical valency, corresponding to the total +number of 2-quantum orbits, is four.</p> + + +<p class="nindc space-above2"> +THE PRODUCTION OF LINE SPECTRA</p> + + +<p>It is not proposed to discuss the theory of the origin of line spectra +here in any detail. What is important from the astrophysical point of +view is the association of known lines in the spectrum with different +levels of energy in the atom, these levels representing definite +electron orbits. Absorption and emission of energy take place in an +atom by the transfer of an electron from an orbit associated with low +energy to an orbit associated with high energy, and vice versa. The +frequency of the light which is thus absorbed or emitted is expressed +by the familiar quantum relation:</p> + +<p> +\[ +E_1 - E_2 = h\nu +\] +where \(E_1\) and \(E_2\) are the initial and final energies, +\(\displaystyle{h = 6.55 \times 10^{-27}\,\text{erg seconds}}\), and +\(\nu\) is the frequency of the light absorbed or given out.</p> + +<p>The atom absorbs from its environment the quanta relevant to the +particular electron transfers of which it is capable at the time. These +transfers are, of course, governed by the number and arrangement of the +spectroscopic valency electrons, or in other words, by the state of +ionization or excitation of the atom.</p> + +<p>The unionized (or neutral) atom in the unexcited state absorbs the +<i>ultimate lines</i> by the removal of one electron from its normal +stationary state to some other which can be reached from that state, +and re-emits them by the return of the electron to that state. The +electron may, of course, leave the state to which it was carried by +the ultimate absorption and pass to some state other than the normal +one. If this final state is a state of higher energy than the previous +state, the line produced by the process will be an absorption line; if +<span class="pagenum" id="Page_12">[Pg 12]</span> +it is of lower energy the result will be the production of an emission +line. In either case the line produced by the transfer of an electron +from a stationary state other than the normal state is known as a +<i>subordinate line</i>. The distinction between series of ultimate +and subordinate lines is of great importance in the astrophysical +applications of the theory of ionization.</p> + +<figure class="figcenter" id="i002"> +<img src="images/i002.jpg" width="2000" height="1234" alt="i002"> +<figcaption class="caption"> + +<p>Figure 2</p> + +<p>The hydrogen atom. The ten innermost orbits possible for the single +electron of the atom of hydrogen are diagrammatically represented. +All possible quantum transitions between the orbits are indicated as +follows:—short dashes, Lyman series, terminating at a 1-quantum orbit; +full lines, Balmer series, terminating at a 2-quantum orbit; long +dashes, Paschen series, terminating at a 3-quantum orbit. Transfers are +only possible between orbits with azimuthal quantum numbers differing +by ±1.</p></figcaption> +</figure> + +<p>When the energy supply from the environment is great enough, +the “outermost” (or most easily detachable) valency electron is +entirely removed by the energy absorbed. In consequence the atom is +superficially transformed, giving rise to a totally new spectrum, +which strongly resembles the spectrum of the atom next preceding in +the periodic system. Bohr’s table embodies the interpretation of +<span class="pagenum" id="Page_13">[Pg 13]</span> +this resemblance—the so-called Displacement Rule of Kossell and +Sommerfeld<a id="FNanchor_7" href="#Footnote_7" class="fnanchor">[7]</a>—which has recently been strikingly confirmed by a very +complete investigation of the arc and spark (neutral and ionized) +spectra of the atoms in the first long period.<a id="FNanchor_8" href="#Footnote_8" class="fnanchor">[8]</a> It may be seen at +once, for instance, that the removal of the outermost (or \(3_2\)) +electron from the atom of aluminum (\(1_3\)) produces an arrangement +of external electrons identical with that for magnesium (\(1_2\)). The +ionized atom produced by the complete removal of one electron gives, +like the neutral atom, two kinds of line spectrum—the ultimate lines +and the subordinate lines.</p> + +<p><span class="pagenum" id="Page_14">[Pg 14]</span></p> + +<figure class="figcenter" id="i003"> +<img src="images/i003.jpg" width="2000" height="1386" alt="i003"> +<figcaption class="caption"> + +<p>Figure 3</p> + +<p>Energy levels for the hydrogen atom. Horizontal lines represent +diagrammatically the levels of energy corresponding to all the possible +electron orbits up to and including those of total quantum number four. +Total quantum numbers are indicated on the left margin, azimuthal +quantum numbers on the right margin. Transitions are only possible +between orbits which differ by ±1 in azimuthal quantum number. All +such possible transitions are indicated in the diagram by heavy lines. +“Forbidden jumps,” for which the difference in azimuthal quantum number +is zero or greater than 1, are indicated by light lines. This diagram +embodies the same relations as <a href="#i002">Figure 2</a>, the levels representing the +various orbits in that figure.</p></figcaption> +</figure> + +<p>Effectively, the ionized atom may be regarded as a new atom altogether. +It reproduces the spectrum of the atom of preceding atomic number, +in cases which have been fully investigated, with great fidelity, +excepting that the Rydberg constant in the series formula is multiplied +by four. For the twice and thrice ionized atoms the same is true, the +Rydberg constant being multiplied by nine and by sixteen in the two +cases. It is scarcely necessary to mention the beautiful confirmation +of the theory that has been furnished by the analyses<a id="FNanchor_9" href="#Footnote_9" class="fnanchor">[9]</a><a id="FNanchor_10" href="#Footnote_10" class="fnanchor">[10]</a> of the +spectra of Na, Mg, and Mg+, Al, Al+, and Al++, and Si, Si+, Si++, +and Si+++. The attribution of the Pickering series (first observed +in the spectrum of \(\zeta\) Puppis) to ionized helium was the first +established example of the displacement rule, and constituted one +of the earliest triumphs of the Bohr theory.<a id="FNanchor_11" href="#Footnote_11" class="fnanchor">[11]</a> The detection and +resolution of the alternate components of that series, which fall very +near to the Balmer lines of hydrogen in the spectra of the hottest +stars, and the consequent derivation of the Rydberg constant for +helium,<a id="FNanchor_12" href="#Footnote_12" class="fnanchor">[12]</a> represents an astrophysical contribution to pure physics +which is of the highest importance.</p> + + +<p class="nindc space-above2"> +IONIZATION AND EXCITATION</p> + + +<p>The <i>ionization potential</i> of an atom is the energy in volts that +is required in order to remove the outermost electron to infinity. The +<i>excitation potential</i> corresponding to any particular spectral +series is the energy in volts that must be imparted to the atom in +the normal state in order that there may be an electron in a suitable +electron orbit for the absorption or emission of that series. Several +different excitation potentials are usually associated with one atom. +The ionization potential and the excitation potentials are collectively +termed the <i>critical potentials</i>.</p> + +<p>From the astrophysical point of view, ionization and excitation +<span class="pagenum" id="Page_15">[Pg 15]</span> +potentials are important as forming the basic data for the Saha theory +of thermal ionization, with which the greater part of this work is +concerned. A list of the ionization potentials hitherto determined is +therefore reproduced in the following table. The first two columns +contain the values obtained by the physical and spectroscopic methods, +respectively. The third column contains “astrophysical estimates,” +which are inserted here to make the table more complete. The derivation +of the astrophysical values will be discussed<a id="FNanchor_13" href="#Footnote_13" class="fnanchor">[13]</a> in <a href="#CHAPTER_XI">Chapter XI</a>. +Physical values result from the direct application of electrical +potentials to the element in question, and spectroscopic values are +derived from the values of the optical terms. (See <a href="#APPENDICES">Appendix</a>.)</p> + +<h2><a id="TABLE_III">TABLE III</a></h2> + +<table class="autotable"> +<thead><tr> +<th class="tdc bb bt2 br" rowspan="2">Atomic <br> +Number </th> +<th class="tdc bb bt2 br" rowspan="2"> Element </th> +<th class="tdc bb bt2 br" colspan="3">Ionization potential</th> +<th class="tdc bb bt2" rowspan="2"> Reference </th> +</tr> +<tr> +<th class="tdc bb br">Physical</th> +<th class="tdc bb br">Spectroscopic</th> +<th class="tdc bb br">Astrophysical</th> +</tr> +</thead> +<tbody><tr> +<td class="tdr br">1 </td> +<td class="tdl br"> H</td> +<td class="tdl br">14.4, 13.3</td> +<td class="tdc br">13.54</td> +<td class="tdc br"> </td> +<td class="tdl"> <a href="#1">1</a>, <a href="#2">2</a>, <a href="#3">3</a></td> +</tr><tr> +<td class="tdr br">2 </td> +<td class="tdl br"> He</td> +<td class="tdl br">25.4</td> +<td class="tdc br">24.47</td> +<td class="tdc br"> </td> +<td class="tdl"> <a href="#5">5</a>, <a href="#4">4</a></td> +</tr><tr> +<td class="tdr br"></td> +<td class="tdl br"> He+</td> +<td class="tdl br">54.3</td> +<td class="tdc br">54.18</td> +<td class="tdc br"> </td> +<td class="tdl"> <a href="#3">3</a>, <a href="#5">5</a></td> +</tr><tr> +<td class="tdr br">3 </td> +<td class="tdl br"> Li</td> +<td class="tdl br"> </td> +<td class="tdc br">5.37</td> +<td class="tdc br"> </td> +<td class="tdl"> <a href="#3">3</a></td> +</tr><tr> +<td class="tdr br"></td> +<td class="tdl br"> Li+</td> +<td class="tdl br">40</td> +<td class="tdc br"></td> +<td class="tdc br"> </td> +<td class="tdl"> <a href="#6">6</a></td> +</tr><tr> +<td class="tdr br">4 </td> +<td class="tdl br"> Be</td> +<td class="tdl br"> </td> +<td class="tdc br">9.6</td> +<td class="tdc br"> </td> +<td class="tdl"> <a href="#7">7</a></td> +</tr><tr> +<td class="tdr br">5 </td> +<td class="tdl br"> B</td> +<td class="tdl br"> </td> +<td class="tdc br">8.3</td> +<td class="tdc br"> </td> +<td class="tdl"> <a href="#7">7</a></td> +</tr><tr> +<td class="tdr br"> </td> +<td class="tdl br"> B+</td> +<td class="tdl br"> </td> +<td class="tdc br">19.0</td> +<td class="tdc br"> </td> +<td class="tdl"> <a href="#7">7</a></td> +</tr><tr> +<td class="tdr br">6 </td> +<td class="tdl br"> C+</td> +<td class="tdl br"> </td> +<td class="tdc br">24.3</td> +<td class="tdc br"> </td> +<td class="tdl"> <a href="#8">8</a></td> +</tr><tr> +<td class="tdr br"> </td> +<td class="tdl br"> C++</td> +<td class="tdl br"> </td> +<td class="tdc br"> </td> +<td class="tdc br">45</td> +<td class="tdl"> <a href="#9">9</a>, <a href="#12">12</a></td> +</tr><tr> +<td class="tdr br">7 </td> +<td class="tdl br"> N</td> +<td class="tdl br">16.9</td> +<td class="tdc br"></td> +<td class="tdc br"> </td> +<td class="tdl"> <a href="#10">10</a></td> +</tr><tr> +<td class="tdr br"> </td> +<td class="tdl br"> N+</td> +<td class="tdl br"></td> +<td class="tdc br"></td> +<td class="tdc br">24</td> +<td class="tdl"> <a href="#9">9</a>, <a href="#12">12</a></td> +</tr><tr> +<td class="tdr br"> </td> +<td class="tdl br"> N++</td> +<td class="tdl br"></td> +<td class="tdc br"></td> +<td class="tdc br">45</td> +<td class="tdl"> <a href="#9">9</a>, <a href="#12">12</a></td> +</tr><tr> +<td class="tdr br">8 </td> +<td class="tdl br"> O</td> +<td class="tdl br">15.5</td> +<td class="tdc br">13.56</td> +<td class="tdc br"> </td> +<td class="tdl"> <a href="#3">3</a>, <a href="#11">11</a></td> +</tr><tr> +<td class="tdr br"> </td> +<td class="tdl br"> O+</td> +<td class="tdl br"></td> +<td class="tdc br"></td> +<td class="tdc br">32</td> +<td class="tdl"> <a href="#9">9</a>, <a href="#12">12</a></td> +</tr><tr> +<td class="tdr br"> </td> +<td class="tdl br"> O++</td> +<td class="tdl br">50</td> +<td class="tdc br"></td> +<td class="tdc br">45</td> +<td class="tdl"> <a href="#12">12</a></td> +</tr><tr> +<td class="tdr br">10 </td> +<td class="tdl br"> Ne</td> +<td class="tdl br">16.7</td> +<td class="tdc br"></td> +<td class="tdc br"> </td> +<td class="tdl"> <a href="#13">13</a></td> +</tr><tr> +<td class="tdr br">11 </td> +<td class="tdl br"> Na</td> +<td class="tdl br">5.13</td> +<td class="tdc br">5.12</td> +<td class="tdc br"> </td> +<td class="tdl"> <a href="#14">14</a>, <a href="#3">3</a></td> +</tr><tr> +<td class="tdr br"> </td> +<td class="tdl br"> Na+</td> +<td class="tdl br">30-35</td> +<td class="tdc br"> </td> +<td class="tdc br"> </td> +<td class="tdl"> <a href="#15">15</a></td> +</tr><tr> +<td class="tdr br">12 </td> +<td class="tdl br"> Mg</td> +<td class="tdl br">7.75</td> +<td class="tdc br">7.61</td> +<td class="tdc br"> </td> +<td class="tdl"> <a href="#16">16</a>, <a href="#3">3</a></td> +</tr><tr> +<td class="tdr br"> </td> +<td class="tdl br"> Mg+</td> +<td class="tdl br"> </td> +<td class="tdc br">14.97</td> +<td class="tdc br"> </td> +<td class="tdl"> <a href="#3">3</a></td> +</tr><tr> +<td class="tdr br">13 </td> +<td class="tdl br"> Al</td> +<td class="tdl br"> </td> +<td class="tdc br">5.96</td> +<td class="tdc br"> </td> +<td class="tdl"> <a href="#3">3</a></td> +</tr><tr> +<td class="tdr br"> </td> +<td class="tdl br"> Al+</td> +<td class="tdl br"> </td> +<td class="tdc br">18.18</td> +<td class="tdc br"> </td> +<td class="tdl"> <a href="#17">17</a></td> +</tr><tr> +<td class="tdr br"></td> +<td class="tdl br"> Al++</td> +<td class="tdl br"> </td> +<td class="tdc br">28.32</td> +<td class="tdc br"> </td> +<td class="tdl"> <a href="#17">17</a></td> +</tr><tr> +<td class="tdr br">14 </td> +<td class="tdl br"> Si</td> +<td class="tdl br"> </td> +<td class="tdc br">10.6</td> +<td class="tdc br">8.5</td> +<td class="tdl"> <a href="#18">18</a>, <a href="#19">19</a></td> +</tr><tr> +<td class="tdr br"></td> +<td class="tdl br"> Si+</td> +<td class="tdl br"> </td> +<td class="tdc br">16.27</td> +<td class="tdc br"></td> +<td class="tdl"> <a href="#18">18</a></td> +</tr><tr> +<td class="tdr br"> </td> +<td class="tdl br"> Si++</td> +<td class="tdl br"> </td> +<td class="tdc br"></td> +<td class="tdc br">31.66</td> +<td class="tdl"> <a href="#18">18</a></td> +</tr><tr> +<td class="tdr br"></td> +<td class="tdl br"> Si+++</td> +<td class="tdl br"> </td> +<td class="tdc br">44.95</td> +<td class="tdc br">8.5</td> +<td class="tdl"> <a href="#18">18</a></td> +</tr><tr> +<td class="tdr br">15 </td> +<td class="tdl br"> P</td> +<td class="tdl br">13.3, 10.3</td> +<td class="tdc br"> </td> +<td class="tdc br"> </td> +<td class="tdl"> <a href="#20">20</a>, <a href="#21">21</a></td> +</tr><tr> +<td class="tdr br"> </td> +<td class="tdl br"> P++</td> +<td class="tdl br"> </td> +<td class="tdc br">29.8</td> +<td class="tdc br"></td> +<td class="tdl"> <a href="#7">7</a></td> +</tr><tr> +<td class="tdr br"></td> +<td class="tdl br"> P+++</td> +<td class="tdl br"> </td> +<td class="tdc br">45.3</td> +<td class="tdc br"></td> +<td class="tdl"> <a href="#7">7</a></td> +</tr><tr> +<td class="tdr br">16 </td> +<td class="tdl br"> S</td> +<td class="tdl br">12.2</td> +<td class="tdc br">10.31</td> +<td class="tdc br"> </td> +<td class="tdl"> <a href="#20">20</a>, <a href="#12">12</a></td> +</tr><tr> +<td class="tdr br"> </td> +<td class="tdl br"> S+</td> +<td class="tdl br"> </td> +<td class="tdc br"></td> +<td class="tdc br">20</td> +<td class="tdl"> <a href="#9">9</a>, <a href="#12">12</a></td> +</tr><tr> +<td class="tdr br"> </td> +<td class="tdl br"> S++</td> +<td class="tdl br"></td> +<td class="tdc br"> </td> +<td class="tdc br">32</td> +<td class="tdl"> <a href="#9">9</a>, <a href="#12">12</a></td> +</tr><tr> +<td class="tdr br"> </td> +<td class="tdl br"> S+++</td> +<td class="tdl br"> </td> +<td class="tdc br">46.8</td> +<td class="tdc br"> </td> +<td class="tdl"> <a href="#7">7</a></td> +</tr><tr> +<td class="tdr br">17 </td> +<td class="tdl br"> Cl</td> +<td class="tdl br">8.2</td> +<td class="tdc br"> </td> +<td class="tdc br"> </td> +<td class="tdl"> <a href="#13">13</a></td> +</tr><tr> +<td class="tdr br">18 </td> +<td class="tdl br"> A</td> +<td class="tdl br">15.1</td> +<td class="tdc br"> </td> +<td class="tdc br"> </td> +<td class="tdl"> <a href="#22">22</a></td> +</tr><tr> +<td class="tdr br"></td> +<td class="tdl br"> A+</td> +<td class="tdl br">33, 34, 41.5</td> +<td class="tdc br"> </td> +<td class="tdc br"> </td> +<td class="tdl"> <a href="#23">23</a>, <a href="#22">22</a>, <a href="#24">24</a></td> +</tr><tr> +<td class="tdr br">19 </td> +<td class="tdl br"> K</td> +<td class="tdl br">4.1</td> +<td class="tdc br">4.32</td> +<td class="tdc br"> </td> +<td class="tdl"> <a href="#14">14</a>, <a href="#3">3</a></td> +</tr><tr> +<td class="tdr br"></td> +<td class="tdl br"> K+</td> +<td class="tdl br">20-23</td> +<td class="tdc br"></td> +<td class="tdc br"> </td> +<td class="tdl"> <a href="#14">14</a></td> +</tr><tr> +<td class="tdr br">20 </td> +<td class="tdl br"> Ca</td> +<td class="tdl br"></td> +<td class="tdc br">6.09</td> +<td class="tdc br"> </td> +<td class="tdl"> <a href="#3">3</a></td> +</tr><tr> +<td class="tdr br"></td> +<td class="tdl br"> Ca+</td> +<td class="tdl br"></td> +<td class="tdc br">11.82</td> +<td class="tdc br"> </td> +<td class="tdl"> <a href="#3">3</a></td> +</tr><tr> +<td class="tdr br">21 </td> +<td class="tdl br"> Sc</td> +<td class="tdl br"></td> +<td class="tdc br"></td> +<td class="tdc br">6-9</td> +<td class="tdl"> <a href="#25">25</a></td> +</tr><tr> +<td class="tdr br"></td> +<td class="tdl br"> Sc+</td> +<td class="tdl br"></td> +<td class="tdc br"></td> +<td class="tdc br">12.5</td> +<td class="tdl"> <a href="#19">19</a></td> +</tr><tr> +<td class="tdr br">22 </td> +<td class="tdl br"> Ti</td> +<td class="tdl br"></td> +<td class="tdc br">6.5</td> +<td class="tdc br"></td> +<td class="tdl"> <a href="#26">26</a></td> +</tr><tr> +<td class="tdr br"></td> +<td class="tdl br"> Ti+</td> +<td class="tdl br"></td> +<td class="tdc br"></td> +<td class="tdc br">12.5</td> +<td class="tdl"> <a href="#19">19</a></td> +</tr><tr> +<td class="tdr br">23 </td> +<td class="tdl br"> V</td> +<td class="tdl br"></td> +<td class="tdc br"></td> +<td class="tdc br">6-9</td> +<td class="tdl"> <a href="#25">25</a></td> +</tr><tr> +<td class="tdr br">24 </td> +<td class="tdl br"> Cr</td> +<td class="tdl br"></td> +<td class="tdc br">6.7</td> +<td class="tdc br"> </td> +<td class="tdl"> <a href="#3">3</a></td> +</tr><tr> +<td class="tdr br">25 </td> +<td class="tdl br"> Mn</td> +<td class="tdl br"></td> +<td class="tdc br">7.41</td> +<td class="tdc br"> </td> +<td class="tdl"> <a href="#35">35</a></td> +</tr><tr> +<td class="tdr br">26 </td> +<td class="tdl br"> Fe</td> +<td class="tdl br"></td> +<td class="tdc br">5.9, 8.15</td> +<td class="tdc br">7.5</td> +<td class="tdl"> <a href="#28">28</a>, <a href="#29">29</a>, <a href="#19">19</a></td> +</tr><tr> +<td class="tdr br"></td> +<td class="tdl br"> Fe</td> +<td class="tdl br"></td> +<td class="tdc br"></td> +<td class="tdc br">13</td> +<td class="tdl"> <a href="#19">19</a></td> +</tr><tr> +<td class="tdr br">27 </td> +<td class="tdl br"> Co</td> +<td class="tdl br"></td> +<td class="tdc br"></td> +<td class="tdc br">6-9</td> +<td class="tdl"> <a href="#25">25</a></td> +</tr><tr> +<td class="tdr br">28 </td> +<td class="tdl br"> Ni</td> +<td class="tdl br"></td> +<td class="tdc br"></td> +<td class="tdc br">6-9</td> +<td class="tdl"> <a href="#25">25</a></td> +</tr><tr> +<td class="tdr br">29 </td> +<td class="tdl br"> Cu</td> +<td class="tdl br"></td> +<td class="tdc br">7.69</td> +<td class="tdc br"></td> +<td class="tdl"> <a href="#3">3</a></td> +</tr><tr> +<td class="tdr br">30 </td> +<td class="tdl br"> Zn</td> +<td class="tdl br"></td> +<td class="tdc br">9.35</td> +<td class="tdc br"></td> +<td class="tdl"> <a href="#3">3</a></td> +</tr><tr> +<td class="tdr br"></td> +<td class="tdl br"> Zn+</td> +<td class="tdl br"></td> +<td class="tdc br">19.59</td> +<td class="tdc br"></td> +<td class="tdl"> <a href="#7">7</a></td> +</tr><tr> +<td class="tdr br">31 </td> +<td class="tdl br"> Ga</td> +<td class="tdl br"></td> +<td class="tdc br">5.97</td> +<td class="tdc br"></td> +<td class="tdl"> <a href="#3">3</a></td> +</tr><tr> +<td class="tdr br">33 </td> +<td class="tdl br"> As</td> +<td class="tdl br">11.5</td> +<td class="tdc br"> </td> +<td class="tdc br"></td> +<td class="tdl"> <a href="#30">30</a></td> +</tr><tr> +<td class="tdr br">34 </td> +<td class="tdl br"> Se</td> +<td class="tdl br">12-13, 11.7</td> +<td class="tdc br"> </td> +<td class="tdc br"></td> +<td class="tdl"> <a href="#31">31</a>, <a href="#32">32</a></td> +</tr><tr> +<td class="tdr br">35 </td> +<td class="tdl br"> Br</td> +<td class="tdl br">1.00</td> +<td class="tdc br"> </td> +<td class="tdc br"></td> +<td class="tdl"> <a href="#13">13</a></td> +</tr><tr> +<td class="tdr br">36 </td> +<td class="tdl br"> Kr</td> +<td class="tdl br">14.5</td> +<td class="tdc br"> </td> +<td class="tdc br"></td> +<td class="tdl"> <a href="#33">33</a></td> +</tr><tr> +<td class="tdr br">37 </td> +<td class="tdl br"> Rb</td> +<td class="tdl br">4.1</td> +<td class="tdc br">4.16</td> +<td class="tdc br"></td> +<td class="tdl"> <a href="#34">34</a>, <a href="#3">3</a> +<span class="pagenum" id="Page_16">[Pg 16]</span></td> +</tr><tr> +<td class="tdr br">38 </td> +<td class="tdl br"> Sr</td> +<td class="tdl br"></td> +<td class="tdc br">5.67</td> +<td class="tdc br"></td> +<td class="tdl"> <a href="#3">3</a></td> +</tr><tr> +<td class="tdr br"></td> +<td class="tdl br"> Sr+</td> +<td class="tdl br"></td> +<td class="tdc br">10.98</td> +<td class="tdc br"></td> +<td class="tdl"> <a href="#3">3</a></td> +</tr><tr> +<td class="tdr br">42 </td> +<td class="tdl br"> Mo</td> +<td class="tdl br"></td> +<td class="tdc br">7.1, 7.35</td> +<td class="tdc br"></td> +<td class="tdl"> <a href="#35">35</a>, <a href="#36">36</a></td> +</tr><tr> +<td class="tdr br">47 </td> +<td class="tdl br"> Ag</td> +<td class="tdl br"></td> +<td class="tdc br">7.54</td> +<td class="tdc br"></td> +<td class="tdl"> <a href="#3">3</a></td> +</tr><tr> +<td class="tdr br">48 </td> +<td class="tdl br"> Cd</td> +<td class="tdl br"></td> +<td class="tdc br">8.95</td> +<td class="tdc br"></td> +<td class="tdl"> <a href="#3">3</a></td> +</tr><tr> +<td class="tdr br"></td> +<td class="tdl br"> Cd+</td> +<td class="tdl br"></td> +<td class="tdc br">18.48</td> +<td class="tdc br"></td> +<td class="tdl"> <a href="#7">7</a></td> +</tr><tr> +<td class="tdr br">49 </td> +<td class="tdl br"> In</td> +<td class="tdl br"></td> +<td class="tdc br">5.75</td> +<td class="tdc br"></td> +<td class="tdl"> <a href="#37">37</a></td> +</tr><tr> +<td class="tdr br">51 </td> +<td class="tdl br"> Sb</td> +<td class="tdl br">8.5 ± 1.0</td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdl"> <a href="#26">26</a></td> +</tr><tr> +<td class="tdr br">53 </td> +<td class="tdl br"> I</td> +<td class="tdl br">10.1, 8.0</td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdl"> <a href="#38">38</a>, <a href="#39">39</a></td> +</tr><tr> +<td class="tdr br">56 </td> +<td class="tdl br"> Ba</td> +<td class="tdl br"></td> +<td class="tdc br">5.19</td> +<td class="tdc br"></td> +<td class="tdl"> <a href="#3">3</a></td> +</tr><tr> +<td class="tdr br"></td> +<td class="tdl br"> Ba+</td> +<td class="tdl br"></td> +<td class="tdc br">9.96</td> +<td class="tdc br"></td> +<td class="tdl"> <a href="#3">3</a></td> +</tr><tr> +<td class="tdr br">80 </td> +<td class="tdl br"> Hg</td> +<td class="tdl br"></td> +<td class="tdc br">10.4</td> +<td class="tdc br"></td> +<td class="tdl"> <a href="#40">40</a></td> +</tr><tr> +<td class="tdr br">81 </td> +<td class="tdl br"> Tl</td> +<td class="tdl br"></td> +<td class="tdc br">6.94</td> +<td class="tdc br"></td> +<td class="tdl"> <a href="#41">41</a></td> +</tr><tr> +<td class="tdr br">82 </td> +<td class="tdl br"> Pb</td> +<td class="tdl br">7.93</td> +<td class="tdc br">7.38</td> +<td class="tdc br"></td> +<td class="tdl"> <a href="#42">42</a></td> +</tr><tr> +<td class="tdr br">83 </td> +<td class="tdl br"> Bi</td> +<td class="tdl br">8.0</td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdl"> <a href="#30">30</a></td> +</tr><tr> +<td class="tdr bb br"></td> +<td class="tdl bb br"> Bi+</td> +<td class="tdl bb br">14.0</td> +<td class="tdc bb br"></td> +<td class="tdc bb br"></td> +<td class="tdl bb"> <a href="#30">30</a> +<span class="pagenum" id="Page_17">[Pg 17]</span></td> +</tr> +</tbody> +</table> + +<p><a id="1">1</a> Horton and Davies, Proc. Roy. Soc., 97A, 1, 1920.</p> + +<p><a id="2">2</a> Mohler and Foote, J. Op. Soc. Am., 4, 49, 1920.</p> + +<p><a id="3">3</a> A. Fowler, Report on Series in Line Spectra, 1922.</p> + +<p><a id="4">4</a> Lyman, Phys. Rev., 21, 202, 1923.</p> + +<p><a id="5">5</a> Horton and Davies, Proc. Roy. Soc., 95A, 408, 1919.</p> + +<p><a id="6">6</a> Mohler, Science, 58, 468, 1923.</p> + +<p><a id="7">7</a> D. R. Hartree, unpub.</p> + +<p><a id="8">8</a> A. Fowler, Proc. Roy. Soc., 105A, 299, 1924.</p> + +<p><a id="9">9</a> Payne, H. C. 256, 1924.</p> + +<p><a id="10">10</a> Brandt, Zeit. f. Phys., 8, 32, 1921.</p> + +<p><a id="11">11</a> Hopfield, Nature, 112, 437, 1923.</p> + +<p><a id="12">12</a> R. H. Fowler and Milne, M. N. R. A. S., 84, 499, 1924.</p> + +<p><a id="13">13</a> Horton and Davies, Proc. Roy. Soc., 98A, 121, 1920.</p> + +<p><a id="14">14</a> Tate and Foote, Phil. Mag., 36, 64, 1918.</p> + +<p><a id="15">15</a> Foote, Meggers, and Mohler, Ap. J., 55, 145, 1922.</p> + +<p><a id="16">16</a> Foote and Mohler, Phil. Mag., 37, 33, 1919.</p> + +<p><a id="17">17</a> Paschen, An. d. Phys., 71, 151 and 537, 1923.</p> + +<p><a id="18">18</a> A. Fowler, Bakerian Lecture, 1924.</p> + +<p><a id="19">19</a> Menzel, H. C. 258, 1924.</p> + +<p><a id="20">20</a> Mohler and Foote, Phys. Rev., 15, 321, 1920.</p> + +<p><a id="21">21</a> Duffendack and Huthsteiner, Amer. Phys. Soc., 1924.</p> + +<p><a id="22">22</a> Horton and Davies, Proc. Roy. Soc., 102A, 131, 1922.</p> + +<p><a id="23">23</a> Shaver, Trans. Roy. Soc. Can., 16, 135, 1922.</p> + +<p><a id="24">24</a> Smyth and Compton, Amer. Phys. Soc., 1925.</p> + +<p><a id="25">25</a> Russell, Ap. J., 55, 119, 1922.</p> + +<p><a id="26">26</a> Kiess and Kiess, J. Op. Soc. Am., 8, 609, 1924.</p> + +<p><a id="27">27</a> Catalan, Phil. Trans., 223A, 1922.</p> + +<p><a id="28">28</a> Sommerfeld, Physica, 4, 115, 1924.</p> + +<p><a id="29">29</a> Gieseler and Grotrian, Zeit. f. Phys., 25, 165, 1924.</p> + +<p><a id="30">30</a> Ruark, Mohler, Foote, and Chenault, Nature, 112, 831, 1923.</p> + +<p><a id="31">31</a> Foote and Mohler, The Origin of Spectra, 67, 1922.</p> + +<p><a id="32">32</a> Udden, Phys. Rev., 18, 385, 1921.</p> + +<p><a id="33">33</a> Sponer, Zeit. f. Phys., 18, 249, 1923.</p> + +<p><a id="34">34</a> Foote, Rognley and Mohler, Phys. Rev., 13, 61, 1919.</p> + +<p><a id="35">35</a> Catalan, C. R., 176, 1063, 1923.</p> + +<p><a id="36">36</a> Kiess, Bur. Stan. Sci. Pap. 474, 113, 1923.</p> + +<p><a id="37">37</a> McLennan, Br. A. Rep., 25, 1923.</p> + +<p><a id="38">38</a> Foote and Mohler, The Origin of Spectra, 67, 1922.</p> + +<p><a id="39">39</a> Smyth and Compton, Phys. Rev., 16, 502, 1920.</p> + +<p><a id="40">40</a> Eldridge, Phys. Rev., 20, 456, 1922.</p> + +<p><a id="41">41</a> Mohler and Ruark, J. Op. Soc. Am., 7, 819, 1923.</p> + +<p><a id="42">42</a> Grotrian, Zeit. f. Phys., 18, 169, 1923.</p> + +<p><span class="pagenum" id="Page_18">[Pg 18]</span></p> + +<p>By the use of one or other of the available methods, the data for +neutral atoms are complete as far as atomic number 38, with the +exception of carbon (6), fluorine (9) and germanium (32). The data +for ionized atoms are also increasing, at the present time, in a +very gratifying manner. The “hot spark” investigations of Millikan +and Bowen,<a id="FNanchor_14" href="#Footnote_14" class="fnanchor">[14]</a> which permit the estimation of the fifth and sixth +ionization potentials of certain light atoms, are not included in +the table. Under the conditions hitherto investigated in the stellar +atmosphere, ionization corresponding to a potential of about fifty +volts is the highest encountered, and accordingly ionization potentials +that greatly exceed this value have no place in the present tabulation +of astrophysically useful data. A knowledge of the higher critical +potentials<a id="FNanchor_15" href="#Footnote_15" class="fnanchor">[15]</a> is, however, of great interest in connection with the +theoretical problems of the far interior of the star.</p> + +<p>There are conspicuous gaps in the table, and it is to be feared +that many of them are likely to remain unfilled. The spectra of the +neutral atoms of carbon, phosphorus, and nitrogen have hitherto defied +analysis, and our knowledge of the corresponding ionization potentials +must therefore depend on physical methods. For carbon, silicon, +and similar refractory materials, such methods are difficult of +application; the same applies to the metals. It is therefore probable +that the ionization potentials of the neutral atoms of several of the +lighter elements, of the platinum metals, and of the rare earths, will +remain unknown or uncertain for some time to come. None of the atoms +thus omitted is of immediate astrophysical importance.</p> + +<p>As shown in the table, the values for the ionized and doubly +ionized light atoms O+, O++, C++, N++, S+, and S++ are deduced only +astrophysically. It may be hoped that the spectra of these atoms will +soon be arranged in series, so that an accurate value of the ionization +potential may be available, in place of the approximate one deduced +from the stellar evidence, for the corresponding absorption lines are +of importance in the spectra of the hotter stars.</p> + +<p><span class="pagenum" id="Page_19">[Pg 19]</span></p> + +<p>The spectroscopic ionization potentials have an advantage over the +physical values, in that the corresponding state of the atom is +known with certainty, whereas physical methods can in general only +<i>detect</i> some critical potential, without assigning it definitely +to a particular transition. For example, it seems likely that in some +cases the first ionization, whether caused by incident radiation or +by electron impacts, corresponds to the loss of an electron by the +<i>molecule</i>: +\[ +E_2 = E_2^{+} + e +\] +where \(E\) represents the atom, and \(e\) the electron. The effect of +increased excitation would then be the decomposition +\[ +E_2^{+} = E^{+} + E +\] +The first reaction would produce the ionized molecule, and the second +would produce the ionized and neutral atoms <i>simultaneously</i>. It +might thus happen that the \(E^{+}\) spectrum could appear without the +previous appearance of the \(E\) spectrum, since all of the element was +present in the form \(E_2\) before ionization.</p> + +<p>The above is only a simple illustrative example of the possible +complexity in the physical determination of ionization potentials. The +interpretation of four successive critical potentials for hydrogen has +been discussed by Franck, Knipping and Krüger,<a id="FNanchor_16" href="#Footnote_16" class="fnanchor">[16]</a> while eight have +been detected by Horton and Davies<a id="FNanchor_17" href="#Footnote_17" class="fnanchor">[17]</a> for the same element. Similarly +Smyth<a id="FNanchor_18" href="#Footnote_18" class="fnanchor">[18]</a> discusses four critical voltages for nitrogen. No explicit +attempt has yet been made to use these facts for the interpretation of +astrophysical data, but they may account for the unexplained absence of +some neutral elements from the cooler stars. The absence is generally +to be attributed, as will be shown in <a href="#CHAPTER_V">Chapter V</a>, to the non-occurrence +of suitable lines in the part of the spectrum usually examined. But +<span class="pagenum" id="Page_20">[Pg 20]</span> +it is possible that the persistence of the molecule has a definite +significance in the case of nitrogen, where the ionization potential is +as high as 16.9 volts.</p> + +<figure class="figcenter" id="i004"> +<img src="images/i004.jpg" width="2000" height="1556" alt="i004"> +<figcaption class="caption"> + +<p>Figure 4</p> + +<p>Relation between ionization potential and position in the periodic +system. Ordinates are ionization potentials in volts, on the equal +but shifted scales indicated alternately on left and right margins. +Abscissae are columns of the periodic table. Physical determinations +of ionization potential are indicated by open circles; dots give +spectroscopic determinations, and crosses denote astrophysical +estimates. Conjectural portions of the curve are indicated by broken +lines, and atoms of unknown ionization potential are enclosed in +parentheses.</p></figcaption> +</figure> + +<p>The increasing completeness of the table of ionization potentials +suggests a re-examination of the relation recently traced by the +writer<a id="FNanchor_19" href="#Footnote_19" class="fnanchor">[19]</a> between ionization potential and atomic number. The +original diagram, in which columns of the periodic table are treated +as abscissae, and the ordinates are ionization potentials on equal but +shifted scales, so that analogous elements fall one below another, is +here reproduced, with the addition of data more recently obtained.</p> + +<p><span class="pagenum" id="Page_21">[Pg 21]</span></p> + +<p>The Displacement Rule of Kossell and Sommerfeld leads us to expect a +pronounced similarity between the line drawn in the diagram from the +point representing one element to that representing the next, and the +corresponding line for the ionized atoms of the same elements, the +latter being shifted one place to the left for each electron removed. +The points for once and twice ionized atoms are inserted into the +diagram on this principle, and the parallelism is found to exist. The +regularities of the diagram and their possible significance (such, for +example, as the pairing of the valency electrons, the second being +harder to remove than the first) were discussed in the original paper. +All the more recent data appear to confirm the conclusion there set +forth, that the relation between ionization potential and atomic number +is very closely the same in each period.</p> + + +<p class="nindc space-above2"> +DURATION OF ATOMIC STATES</p> + + +<p>In addition to the critical potentials, which give a measure of the +ease with which an atom is excited or ionized, astrophysical theory +requires an estimate of the readiness with which an atom recovers after +excitation or ionization. It appears probable that this factor, like +the critical potentials, is independent of external conditions, and +depends upon something that is intrinsic in the atomic structure. The +“life” of the atom has been extensively investigated in the laboratory, +and has been shown to be a small fraction of a second in duration. +Probably this subject of “atomic lives” is still in an initial stage, +and the accuracy of the results and the range of elements discussed +will be greatly increased in the near future. A summary of the material +obtained up to the present time is contained in the following table. +Successive columns contain the atom discussed, the deduced atomic life +in seconds, the authority, and the reference.</p> + +<p>The data are practically confined to hydrogen and mercury, and for +both these elements the atomic life appears to be of the order +<span class="pagenum" id="Page_22">[Pg 22]</span> +\(\displaystyle{10^{-8}~\text{seconds}}\).</p> + +<p>Astrophysical estimates of the life of the excited calcium atom +have been made by Milne,<a id="FNanchor_20" href="#Footnote_20" class="fnanchor">[20]</a> who derives values of the order +\(\displaystyle{10^{-8}~\text{seconds}}\). This is so near to the +values obtained in the laboratory that it seems permissible, in +the absence of further precise data, to assume an atomic life of +\(\displaystyle{10^{-8}~\text{seconds}}\), as a working hypothesis, +for all atoms. The same value is unlikely to obtain for all atoms; in +particular it may be expected to differ for atoms in different states +of ionization. But here astrophysics must be entirely dependent on +further laboratory work for the determination of a quantity that is of +fundamental importance.</p> + +<h2><a id="TABLE_IV">TABLE IV</a></h2> +<table class="autotable"> +<thead><tr> +<th class="tdc bb bt2 br">Atom</th> +<th class="tdc bb bt2 br">Life</th> +<th class="tdc bb bt2 br">Authority</th> +<th class="tdc bb bt2">Reference</th> +</tr> +</thead> +<tbody><tr> +<td class="tdl br">\(H_\alpha\)</td> +<td class="tdl br">\(1.5\,\times\, 10^{-8}\)</td> +<td class="tdl br">Wien</td> +<td class="tdl">An. d. Phys., 60, 597, 1919</td> + </tr><tr> +<td class="tdl br">\(H_\beta\)</td> +<td class="tdl br">\(1.6\,\times\, 10^{-8}\)</td> +<td class="tdl br">Ibid.</td> +<td class="tdl">Ibid.</td> + </tr><tr> +<td class="tdl br">\(H_\gamma\)</td> +<td class="tdl br">\(1.6\,\times\, 10^{-8}\)</td> +<td class="tdl br">Ibid.</td> +<td class="tdl">Ibid.</td> + </tr><tr> +<td class="tdl br">\(O+\)</td> +<td class="tdl br">\(1.5\,\times\, 10^{-8}\)</td> +<td class="tdl br">Ibid.</td> +<td class="tdl">Ibid.</td> + </tr><tr> +<td class="tdl br">\(H_\beta\)</td> +<td class="tdl br">\(5\,\,\times\, 10^{-8}\)</td> +<td class="tdl br">Dempster</td> +<td class="tdl">Phys. Rev., 15, 138, 1920</td> + </tr><tr> +<td class="tdl br">\(Hg\)</td> +<td class="tdl br">\(7\,\,\times\, 10^{-5}\)</td> +<td class="tdl br">Wood</td> +<td class="tdl">Proc. Roy. Soc., 99A, 362, 1921</td> + </tr><tr> +<td class="tdl br">\(H\)g</td> +<td class="tdr br">\(10^{-8}\)</td> +<td class="tdl br">Franck and Grotian</td> +<td class="tdl">Zeit. f. Phys., 4, 89, 1921</td> + </tr><tr> +<td class="tdl br">\(H_\beta\), \(H_\gamma\)</td> +<td class="tdl br">\(2.3\,\times\, 10^{-8}\)</td> +<td class="tdl br">Mie</td> +<td class="tdl">An. d. Phys., 66, 237, 1921</td> + </tr><tr> +<td class="tdl br">\(H_\beta\), \(H_\gamma\)</td> +<td class="tdl br">\(2.3\,\times\, 10^{-8}\)</td> +<td class="tdl br">Wien</td> +<td class="tdl">An. d. Phys., 66, 232, 1921</td> + </tr><tr> +<td class="tdl br">\(N\) bands</td> +<td class="tdl br">\(3.1\,\times\, 10^{-8}\)</td> +<td class="tdl br">Ibid.</td> +<td class="tdl">Ibid.</td> + </tr><tr> +<td class="tdl br">\(H_\alpha\), \(H_\beta\)</td> +<td class="tdl br">\(1.8\,\times\, 10^{-8}\)</td> +<td class="tdl br">Ibid.</td> +<td class="tdl">An. d. Phys., 73, 483, 1924</td> + </tr><tr> +<td class="tdl br">\(He_{4478}\)</td> +<td class="tdl br">\(1.8\,\times\, 10^{-8}\)</td> +<td class="tdl br">Ibid.</td> +<td class="tdl">Ibid.</td> + </tr><tr> +<td class="tdl br">\(Hg_{4358}\)</td> +<td class="tdl br">\(1.8\,\times\, 10^{-8}\)</td> +<td class="tdl br">Ibid.</td> +<td class="tdl">Ibid.</td> + </tr><tr> +<td class="tdl br">\(Hg_{2536}\)</td> +<td class="tdl br">\(9.7\,\times\, 10^{-8}\)</td> +<td class="tdl br">Ibid.</td> +<td class="tdl">Ibid.</td> + </tr><tr> +<td class="tdl br">\(Hg\)</td> +<td class="tdr br">\(10^{-7}\)</td> +<td class="tdl br">Turner</td> +<td class="tdl">Phys. Rev., 23, 464, 1924</td> + </tr><tr> +<td class="tdl br bb">\(Hg\)</td> +<td class="tdr br bb">\(10^{-6}\)</td> +<td class="tdl br bb">Webb</td> +<td class="tdl bb">Phys. Rev., 21, 464, 1923</td> + </tr> + </tbody> +</table> + + +<p class="nindc space-above2"> +RELATIVE PROBABILITIES OF ATOMIC STATES</p> + + +<p>The relative intensities of lines in a spectrum must depend +fundamentally upon the relative tendencies of the atom to be in the +corresponding states. To a subject which, like astrophysics, depends +<span class="pagenum" id="Page_23">[Pg 23]</span> +for its data largely upon the relative intensities of spectral lines, +the theory of the relative probabilities of atomic states is of extreme +importance. The question is obviously destined to become an important +branch of spectrum theory. It has been discussed, from various +aspects, by Füchtbauer and Hoffmann,<a id="FNanchor_21" href="#Footnote_21" class="fnanchor">[21]</a> Einstein,<a id="FNanchor_22" href="#Footnote_22" class="fnanchor">[22]</a> +Füchtbauer,<a id="FNanchor_23" href="#Footnote_23" class="fnanchor">[23]</a> +Kramers,<a id="FNanchor_24" href="#Footnote_24" class="fnanchor">[24]</a> Coster,<a id="FNanchor_25" href="#Footnote_25" class="fnanchor">[25]</a> +Fermi,<a id="FNanchor_26" href="#Footnote_26" class="fnanchor">[26]</a> and Sommerfeld.<a id="FNanchor_27" href="#Footnote_27" class="fnanchor">[27]</a> The comparison +with observation has been made, up to the present, only for a few +elements. The relative intensities of the fine-structure components +of the Balmer series of hydrogen were examined by Sommerfeld,<a id="FNanchor_28" href="#Footnote_28" class="fnanchor">[28]</a> and +exhaustive work with the calcium spectrum has recently been carried out +by Dorgelo.<a id="FNanchor_29" href="#Footnote_29" class="fnanchor">[29]</a> The astrophysical application of the data bearing on +relative intensities of lines in the spectrum of one and the same atom, +while an essential branch of the subject, is a refinement which belongs +to the future rather than to the present.</p> + + +<p class="nindc space-above2"> +EFFECT ON THE SPECTRUM OF CONDITIONS AT THE SOURCE</p> + +<p>(a) <i>Temperature Class.</i>—It is found experimentally that the +relative intensities of the lines in the spectrum of a substance are +altered when the temperature is changed. Some lines, notably the +ultimate lines mentioned in a previous paragraph, predominate at low +temperature. Other lines, which are weak under these conditions, +become stronger if the temperature is raised, and lines which are the +characteristic feature of the spectrum at the highest temperatures +that can be attained in the furnace are often imperceptible at the +outset. The effects are more conspicuous, and have been most widely +studied, in the spectra of the metals, which are rich in lines and are +amenable to furnace conditions. The results of such experiments, which +<span class="pagenum" id="Page_24">[Pg 24]</span> +are chiefly the work of A. S. King, are expressed by the assignment +of a “temperature class,” ranging from I to V, to each line; Class I +represents the lines characteristic of the lowest temperatures, and +Class V denotes the lines that require the greatest stimulation.</p> + +<p>The temperature class of a line is intimately connected with the +amount of energy required to excite the line. It may, indeed, be +used as a rough criterion of excitation potential, high temperature +class indicating high excitation energy. The temperature class is +therefore useful in assigning series relations to unclassified lines, +and is of value to the astrophysicist chiefly in this capacity of a +classification criterion. King’s work on silicon shows, for instance, +that 3906 is of Class II, and is therefore not an ultimate line—a +fact which has considerable significance in studying the astrophysical +behavior of the line.</p> + +<p>The correlation of temperature class with excitation potential receives +an immediate explanation in terms of the theory of thermal ionization. +It furnishes a useful laboratory corroboration of the theory by showing +that the thermal excitation of successive lines, with rising excitation +potential, takes place in qualitative agreement with prediction.</p> + +<p>The appended list shows the atoms for which the spectra have been +analyzed by King on the basis of temperature class:</p> + +<table class="autotable"> +<thead><tr> +<th class="tdc">Element </th> +<th class="tdc">Reference</th> +<th class="tdc">Element </th> +<th class="tdc">Reference</th> +</tr> +</thead> +<tbody><tr> +<td class="tdl">Iron</td> +<td class="tdl">Mt. W. Contr. 66, 1912</td> +<td class="tdl">Calcium</td> +<td class="tdl">Mt. W. Contr. 150, 1918</td> + </tr><tr> +<td class="tdl">Titanium</td> +<td class="tdl">Mt. W. Contr. 76, 1914</td> +<td class="tdl">Strontium</td> +<td class="tdl">Ibid.</td> + </tr><tr> +<td class="tdl">Vanadium</td> +<td class="tdl">Mt. W. Contr. 94, 1914</td> +<td class="tdl">Barium</td> +<td class="tdl">Ibid.</td> + </tr><tr> +<td class="tdl">Chromium</td> +<td class="tdl">Ibid.</td> +<td class="tdl">Magnesium</td> +<td class="tdl">Ibid.</td> + </tr><tr> +<td class="tdl">Cobalt</td> +<td class="tdl">Mt. W. Contr. 108, 1915</td> +<td class="tdl">Manganese</td> +<td class="tdl">Mt. W. Contr. 198, 1920</td> + </tr><tr> +<td class="tdl">Nickel</td> +<td class="tdl">Ibid.</td> +<td class="tdl">Silicon</td> +<td class="tdl">Pub. A. S. P., 22, 106, 1921</td> + </tr> + </tbody> +</table> + +<p>(b) <i>Pressure.</i>—In the laboratory the observed effects of +pressure<a id="FNanchor_30" href="#Footnote_30" class="fnanchor">[30]</a> are a widening and shifting of the lines in the +spectrum—effects which differ in magnitude and direction for different +lines. The phenomena are well marked under pressures of several +atmospheres.</p> + +<p><span class="pagenum" id="Page_25">[Pg 25]</span></p> + +<p>Recent developments of astrophysics, such as are summarized in +<a href="#CHAPTER_III">Chapter III</a> and <a href="#CHAPTER_IX">Chapter IX</a>, have shown that the pressures in stellar +atmospheres are normally of the order of a hundred dynes per square +centimeter, or less. At such pressures no appreciable pressure shifts +will occur, and indeed one of the most direct methods by which these +exceedingly low pressures in reversing layers have been established<a id="FNanchor_31" href="#Footnote_31" class="fnanchor">[31]</a> +is based on the absence of appreciable pressure effects.</p> + +<p>(c) <i>Zeemann Effect.</i>—The magnetic resolution of spectral lines +into polarized components<a id="FNanchor_32" href="#Footnote_32" class="fnanchor">[32]</a> has, as yet, for the astrophysicist, +chiefly a value as a criterion for classifying spectra. In the field of +solar physics proper, a direct study of the Zeemann effect has led to +important results.<a id="FNanchor_33" href="#Footnote_33" class="fnanchor">[33]</a> The present study is not, however, explicitly +concerned with the sun, except in comparing solar features with similar +features that can also be examined in the stars.</p> + +<p>The investigations of Landé on term structure and Zeemann effect<a id="FNanchor_34" href="#Footnote_34" class="fnanchor">[34]</a> +for multiplets have shown how the Zeemann pattern formed by the +components into which a line is magnetically resolved can be related +to the series attribution of the line. This provides a method of +classifying spectra which are rich in multiplets, and which have +previously defied analysis. The indirect astrophysical value of the +Zeemann effect is, therefore, very great.</p> + +<p>(d) <i>Stark Effect.</i>—The effect of an electric field in resolving +spectral lines into polarized components was first pointed out by +Stark<a id="FNanchor_35" href="#Footnote_35" class="fnanchor">[35]</a> for hydrogen and helium. Several other investigators have +since studied the effect for these two elements,<a id="FNanchor_36" href="#Footnote_36" class="fnanchor">[36]</a> and for +<span class="pagenum" id="Page_26">[Pg 26]</span> +various metals.<a id="FNanchor_37" href="#Footnote_37" class="fnanchor">[37]</a><a id="FNanchor_38" href="#Footnote_38" class="fnanchor">[38]</a> Unlike the temperature and magnetic effects, the Stark +effect has not been used as a criterion for the series relations of +unclassified lines.</p> + +<p>The Stark effect has not been detected in the solar spectrum, +presumably because the concentration of free electrons prevents the +formation of large electrostatic fields.</p> + +<p>Several investigators, however, have contemplated in the Stark effect +a possible factor influencing the stellar spectrum.<a id="FNanchor_39" href="#Footnote_39" class="fnanchor">[39]</a><a id="FNanchor_40" href="#Footnote_40" class="fnanchor">[40]</a> It does +not seem unlikely that nuclear fields could operate as a sensible +general electrostatic field at the photospheric level, thus producing +a widening and winging of certain lines. The question has been +numerically discussed by Hulburt,<a id="FNanchor_41" href="#Footnote_41" class="fnanchor">[41]</a> and Russell and Stewart,<a id="FNanchor_42" href="#Footnote_42" class="fnanchor">[42]</a> in +an examination of Hulburt’s work, concluded that the Stark effect might +possibly make some contribution (probably not a preponderant one) to +the observed widths of lines in the solar spectrum. The question is +not definitely settled, but it appears well to keep so important a +possibility in mind.</p> + + +<div class="footnotes"><h3>FOOTNOTES:</h3> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_1" href="#FNanchor_1" class="label">[1]</a> +International Atomic Weights, 1917.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_2" href="#FNanchor_2" class="label">[2]</a> +Aston, Isotopes, 1922; Phil. Mag., 47, 385, 1924; Nature, +113, 192, 856, 1924; <i>Ibid.</i>, 114, 273, 716, 1924. Products of +radioactive disintegration are omitted.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_3" href="#FNanchor_3" class="label">[3]</a> +Clarke and Washington, Proc. N. Ac. Sci., 8, 108, 1922.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_4" href="#FNanchor_4" class="label">[4]</a> +Bohr, Naturwiss., 11, 619, 1923.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_5" href="#FNanchor_5" class="label">[5]</a> +Sommerfeld, Atombau und Spektrallinien, 3d. edition, 286, +1922.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_6" href="#FNanchor_6" class="label">[6]</a> +A. Fowler, Proc. Roy. Soc., 105A, 299, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_7" href="#FNanchor_7" class="label">[7]</a> +Sommerfeld, Atombau und Spektrallinien, 3d edition, 457, +1922.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_8" href="#FNanchor_8" class="label">[8]</a> +Meggers, Kiess, and Walters, J. Op. Soc. Am., 9, 355, +1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_9" href="#FNanchor_9" class="label">[9]</a> +A. Fowler, Report on Series in Line Spectra, 1922; +Bakerian Lecture, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_10" href="#FNanchor_10" class="label">[10]</a> +Paschen, An. d. Phys., 71, 151, 1923.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_11" href="#FNanchor_11" class="label">[11]</a> +Sommerfeld, Atombau und Spektrallinien, 3d. edition, +255, 1922; A. Fowler, Proc. Roy. Soc., 90A, 426, 1913; Paschen, An. d. +Phys., 50, 901, 1919.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_12" href="#FNanchor_12" class="label">[12]</a> +H. H. Plaskett, Pub. Dom. Ap. Obs., 1, 348, 1922.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_13" href="#FNanchor_13" class="label">[13]</a> +<a href="#Page_156">P. 156</a>.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_14" href="#FNanchor_14" class="label">[14]</a> +Millikan and Bowen, Phys. Rev., 23, 1, 1924; Nature, 114, +380, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_15" href="#FNanchor_15" class="label">[15]</a> +Hartree, Proc. Camb. Phil. Soc., 22, 464, 1924; Thomas, +Phys. Rev., 25, 322, 1925.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_16" href="#FNanchor_16" class="label">[16]</a> +Verh. d. Deutsch. Phys. Ges., 21, 728, 1919.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_17" href="#FNanchor_17" class="label">[17]</a> +Phil. Mag., 46, 872, 1923.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_18" href="#FNanchor_18" class="label">[18]</a> +Proc. Roy. Soc., 103A, 121, 1923.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_19" href="#FNanchor_19" class="label">[19]</a> +Proc. N. Ac. Sci., 10, 322, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_20" href="#FNanchor_20" class="label">[20]</a> +Proc. Phys. Soc. Lond., 36, 94, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_21" href="#FNanchor_21" class="label">[21]</a> +An. d. Phys., 43, 96, 1914.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_22" href="#FNanchor_22" class="label">[22]</a> +Phys. Zeit., 18, 121, 1917.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_23" href="#FNanchor_23" class="label">[23]</a> +Phys. Zeit., 21, 322, 1922.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_24" href="#FNanchor_24" class="label">[24]</a> +Proc. Copenhagen Ac., 1919.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_25" href="#FNanchor_25" class="label">[25]</a> +Physica, 4, 337, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_26" href="#FNanchor_26" class="label">[26]</a> +Physica, 4, 340, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_27" href="#FNanchor_27" class="label">[27]</a> +Zeit. f. Tech. Phys., 5, 2, 1925.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_28" href="#FNanchor_28" class="label">[28]</a> +Atombau und Spektrallinien, 3d edition, 588, 1922.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_29" href="#FNanchor_29" class="label">[29]</a> +Physica, 3, 188, 1923; Zeit. f. Phys., 13, 206, 1923; +<i>ibid.</i>, 22, 270, 1924; Dissertation, Utrecht, 1924; Physica, 5, +27, 1925.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_30" href="#FNanchor_30" class="label">[30]</a> +King, Mt. W. Contr. 53, 1911; <i>ibid.</i>, 60, 1912.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_31" href="#FNanchor_31" class="label">[31]</a> +St. John and Babcock, Ap. J., 60, 32, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_32" href="#FNanchor_32" class="label">[32]</a> +Zeemann, Researches in Magneto-Optics, 1911.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_33" href="#FNanchor_33" class="label">[33]</a> +Hale, Mt. W. Contr. 30, 1908.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_34" href="#FNanchor_34" class="label">[34]</a> +Landé, Zeit. f. Phys., 15, 189, 1923.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_35" href="#FNanchor_35" class="label">[35]</a> +Stark, Elektrische Spektralanalyse Chemischer Atome, +1914.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_36" href="#FNanchor_36" class="label">[36]</a> +Merton, Proc. Roy. Soc., 92A, 322, 1915; <i>ibid.</i>, +95A, 33, 1919.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_37" href="#FNanchor_37" class="label">[37]</a> +Anderson, Mt. W. Contr. 134, 1917.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_38" href="#FNanchor_38" class="label">[38]</a> +Takamine, Mt. W. Contr. 169, 1919.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_39" href="#FNanchor_39" class="label">[39]</a> +Evershed, Observatory, 45, 166, 1922; <i>ibid.</i>, 45, +296, 1922.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_40" href="#FNanchor_40" class="label">[40]</a> +Lindemann, Observatory, 45, 167, 1922.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_41" href="#FNanchor_41" class="label">[41]</a> +Hulburt, Ap. J., 59, 177, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_42" href="#FNanchor_42" class="label">[42]</a> +Russell and Stewart, Ap. J., 59, 197, 1924.</p> + +</div> +</div> + +<hr class="chap x-ebookmaker-drop"> + +<div class="chapter"> +<p><span class="pagenum" id="Page_27">[Pg 27]</span></p> + +<h2 class="nobreak" id="CHAPTER_II">CHAPTER II<br> +THE STELLAR TEMPERATURE SCALE</h2> +</div> + + +<p class="nind"> +IT is well to distinguish the different meanings that are to be +associated with the term “stellar temperature.” The observed energy +distribution in the spectrum, combined with the theory of black-body +radiation, lead to a quantity known as the “effective temperature” +of the star. This is the temperature of a hypothetical black body, +the spectrum of which would have the observed energy distribution of +the star in question. It has often been emphasized that the effective +temperature is merely a label, for it is not the actual temperature of +any specific portion of the star. Presumably the temperature of a star +falls off, from the center outwards, according to the laws expressed +by the theory of radiative equilibrium, and though it might thus be +possible to specify, on certain assumptions, the depth in a star at +which the effective temperature coincides with the actual temperature, +no observational significance could attach to the information.</p> + +<p>The theory of radiative equilibrium<a id="FNanchor_43" href="#Footnote_43" class="fnanchor">[43]</a> enables us to specify the +temperature gradient, and in particular to determine the central +temperature, the effective temperature, and the boundary temperature, +corresponding to a given energy output. These three quantities are +essentially arbitrary, and the second is the only one susceptible +of direct measurement, while none of them represents the actual +temperature of any assignable region. In order to clarify ideas it is +useful to regard the effective temperature as representing roughly +the temperature of the photosphere, that is, of the region in the +star that gives rise to the approximately black continuous background +of the spectrum. It must, however, be remembered that “the theory +provides a definite relation between temperature and optical depth, +involving only one constant, the effective temperature. Suppose now ... +<span class="pagenum" id="Page_28">[Pg 28]</span> +we arbitrarily select a certain temperature, and name it the +photospheric temperature, and name the unknown depth at which it +occurs the photospheric depth; this depth will be described by some +unknown transmission coefficient, to be determined. If, taking account +of absorption and emission, we proceed to calculate the transmission +coefficient ... we shall simply recover the optical depth predicted +by Schwarzschild’s theory.” (Milne.)<a id="FNanchor_44" href="#Footnote_44" class="fnanchor">[44]</a> No method of measuring the +effective temperatures of the stars by comparing their energy spectrum +with that of a black body can remove the arbitrariness of the quantity +thus measured.</p> + +<p>The theory of thermal ionization permits estimates to be made of the +temperatures in the reversing layers of stars. These temperatures +refer to the average level at which are situated the absorbing atoms +corresponding to the lines used. The differences of effective level<a id="FNanchor_45" href="#Footnote_45" class="fnanchor">[45]</a> +for different atoms render these “ionization temperatures” difficult +to define consistently, but they represent actual temperatures of +assignable regions in the star, and the extent of their agreement +with the temperatures derived from the distribution of energy in the +continuous spectrum is a matter of extreme interest. The material +and theory from which the ionization temperatures are derived is the +subject matter of <a href="#CHAPTER_VI">Chapters VI</a> to <a href="#CHAPTER_IX">IX</a>. The temperature scale used in +calibration and in the discussion of the theory of thermal ionization +is the scale derived from the measured <i>effective temperatures</i>.</p> + +<p>The derivation of a definitive scale of effective temperatures from +the numerous available observations is probably impossible at the +present time. The methods employed differ widely, and the conditions +for accurate intercomparison cannot be regarded as fully established. +The material at present available, however, permits some general +conclusions, and as the needs of astrophysics demand a <i>working</i> +temperature scale, such conclusions are summarized in the present +chapter.</p> + +<p><span class="pagenum" id="Page_29">[Pg 29]</span></p> + +<p>In the discussion of the material a difficulty immediately arises. +The scale to be derived must be based entirely, in the present stage +of the observations, upon the apparently brighter stars, and it is +notorious that they are not homogeneous in absolute magnitude. Theory +predicts<a id="FNanchor_46" href="#Footnote_46" class="fnanchor">[46]</a> that absolutely bright stars will have a lower effective +temperature than stars of low luminosity belonging to the same spectral +class, and this prediction is, on the whole, verified by observation. +The material must therefore be selected on the basis of luminosity +if a standard temperature scale is to be formed, and probably the +temperature scale to be aimed at should refer to stars of some one +absolute magnitude adopted as standard. Theoretically, standard mass +might be preferable to standard luminosity, but, in the present state +of the subject, so few masses are known that such a system would not be +practicable. The ideal of referring to standard absolute magnitude was +not attained by the earlier temperature scales, which were apparently +based upon averages for all the available brighter stars.</p> + +<p>The more comprehensive data for the study of the stellar temperature +scale are the spectrophotometric measures of Wilsing and Scheiner,<a id="FNanchor_47" href="#Footnote_47" class="fnanchor">[47]</a> +of Wilsing,<a id="FNanchor_48" href="#Footnote_48" class="fnanchor">[48]</a> of E. S. King,<a id="FNanchor_49" href="#Footnote_49" class="fnanchor">[49]</a> +and of Rosenberg.<a id="FNanchor_50" href="#Footnote_50" class="fnanchor">[50]</a> The +temperature scales derived by Wilsing and by Rosenberg differ by a +linear factor; Rosenberg assigns higher temperatures to the hotter +stars, and lower temperatures to the cooler stars. These temperature +scales, and their intercomparison, have been very fully discussed by +Brill,<a id="FNanchor_51" href="#Footnote_51" class="fnanchor">[51]</a> who reduces all the measures to the scale given by Wilsing, +and gives, for the principal Draper classes, the following comparative +table for the corrected mean effective temperatures on the absolute +centigrade scale.</p> + +<p>In addition to the comprehensive data just quoted, there have been +<span class="pagenum" id="Page_30">[Pg 30]</span> +numerous determinations of the temperatures of individual bright +stars, chiefly by Abbot,<a id="FNanchor_52" href="#Footnote_52" class="fnanchor">[52]</a> Coblentz,<a id="FNanchor_53" href="#Footnote_53" class="fnanchor">[53]</a> +Sampson,<a id="FNanchor_54" href="#Footnote_54" class="fnanchor">[54]</a> and H. H. +Plaskett.<a id="FNanchor_55" href="#Footnote_55" class="fnanchor">[55]</a> In the main these values confirm the scale given in <a href="#TABLE_V">Table V</a>, but sometimes considerable differences occur in the values given for +individual stars by different investigators. At the same time, each +observer is usually reasonably self-consistent, and the deviations must +therefore be ascribed to differences of method. Some of the results are +reproduced, for illustration, in <a href="#TABLE_VI">Table VI</a>.</p> + +<h2><a id="TABLE_V">TABLE V</a></h2> +<table class="autotable"> +<thead><tr> +<th class="tdc">Class </th> +<th class="tdc">Wilsing </th> +<th class="tdc">Rosenberg</th> +<th class="tdc_ws1_sa1">E.S. King<br> +Color Temperature </th> +<th class="tdc_ws1_sa1">E.S. King<br> +Total Radiation</th> +</tr> +</thead> +<tbody><tr> +<td class="tdl">\(B_0\)</td> +<td class="tdc">12300°</td> +<td class="tdc">30000°</td> +<td class="tdc">22700°</td> +<td class="tdc">22700°</td> + </tr><tr> +<td class="tdl">\(B_5\)</td> +<td class="tdc">11450 </td> +<td class="tdc">18000 </td> +<td class="tdc">15200 </td> +<td class="tdc">14900 </td> + </tr><tr> +<td class="tdl">\(A_0\)</td> +<td class="tdc">10250 </td> +<td class="tdc"> 1200</td> +<td class="tdc">11600 </td> +<td class="tdc">11300 </td> + </tr><tr> +<td class="tdl">\(A_5\)</td> +<td class="tdc"> 9000</td> +<td class="tdc"> 9000</td> +<td class="tdc"> 8800</td> +<td class="tdc"> 8600</td> + </tr><tr> +<td class="tdl">\(F_0\)</td> +<td class="tdc"> 7950</td> +<td class="tdc"> 7850</td> +<td class="tdc"> 7900</td> +<td class="tdc"> 7700</td> + </tr><tr> +<td class="tdl">\(F_5\)</td> +<td class="tdc"> 6880</td> +<td class="tdc"> 6930</td> +<td class="tdc"> 7000</td> +<td class="tdc"> 6800</td> + </tr><tr> +<td class="tdl">\(G_0\)</td> +<td class="tdc"> 5980</td> +<td class="tdc"> 6000</td> +<td class="tdc"> 6040</td> +<td class="tdc"> 5870</td> + </tr><tr> +<td class="tdl">\(G_5\)</td> +<td class="tdc"> 5250</td> +<td class="tdc"> 5200</td> +<td class="tdc"> 5090</td> +<td class="tdc"> 4950</td> + </tr><tr> +<td class="tdl">\(K_0\)</td> +<td class="tdc"> 4570</td> +<td class="tdc"> 4570</td> +<td class="tdc"> 4570</td> +<td class="tdc"> 4440</td> + </tr><tr> +<td class="tdl">\(K_5\)</td> +<td class="tdc"> 3860</td> +<td class="tdc"> 3840</td> +<td class="tdc"> 3640</td> +<td class="tdc"> 3550</td> + </tr><tr> +<td class="tdl">\(M_a\)</td> +<td class="tdc"> 3550</td> +<td class="tdc"> 3580</td> +<td class="tdc"> 3430</td> +<td class="tdc"> 3340</td> + </tr> + </tbody> +</table> + +<p>It is seen that the effective temperatures of individual hotter +stars vary widely among themselves. This is largely a result of the +difficulty of making the appropriate correction for atmospheric +extinction. It must, then, be supposed that the temperatures derived by +spectrophotometric methods are not trustworthy for stars hotter than +Class \(A_5\). The values determined by the earlier observers for the +\(A\) and \(B\) classes are almost certainly too low. Rosenberg’s value +of 30,000° for \(B_0\) is, however, most probably too high, as will be +inferred later from the ionization temperature scale.</p> + +<p>For the cooler stars small discrepancies also occur among the different +observers. In the writer’s opinion, the lowest estimates for the +<span class="pagenum" id="Page_31">[Pg 31]</span> +temperatures of the cooler stars are probably nearest to the truth.</p> + +<h2><a id="TABLE_VI">TABLE VI</a></h2> + +<table class="autotable"> +<thead><tr> +<th class="tdc" colspan="2">Star</th> +<th class="tdc_ws1_sa1">Abott<br> +Radiometric </th> +<th class="tdc_ws1_sa1">Coblentz<br> +Thermoelectric</th> +<th class="tdc_ws1_sa1">Plaskett<br> +Wedge Method </th> +<th class="tdc_ws1_sa1">Sampson<br> +Photoelectric</th> +</tr> +</thead> +<tbody><tr> +<td class="tdl">\(\epsilon\)</td> +<td class="tdc">Ori(\(B_0\))</td> +<td class="tdc"></td> +<td class="tdc">13000°</td> +<td class="tdc"></td> +<td class="tdc">25000°</td> + </tr><tr> +<td class="tdl">\(\gamma\)</td> +<td class="tdc">Cas(\(B_{0p}\))</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc">15000°</td> +<td class="tdc">30000 </td> + </tr><tr> +<td class="tdl">\(\epsilon\)</td> +<td class="tdc">Per(\(B_0\))</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc">15000 </td> +<td class="tdc">14000</td> + </tr><tr> +<td class="tdl">\(\beta\)</td> +<td class="tdc">Ori(\(B_8\))</td> +<td class="tdc">16000°</td> +<td class="tdc">10000 </td> +<td class="tdc"></td> +<td class="tdc">14800</td> + </tr><tr> +<td class="tdl">\(\alpha\)</td> +<td class="tdc">Lyr(\(A_0\))</td> +<td class="tdc">14000 </td> +<td class="tdc"> 8000</td> +<td class="tdc"></td> +<td class="tdc">11600</td> + </tr><tr> +<td class="tdl">\(\alpha\)</td> +<td class="tdc">\(CM_a\)(\(A_0\))</td> +<td class="tdc">11000</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc">12800</td> + </tr><tr> +<td class="tdl">(\(\alpha\)</td> +<td class="tdc">Cyg(\(A_{2p}\))</td> +<td class="tdc"></td> +<td class="tdc"> 9000</td> +<td class="tdc"> 9000</td> +<td class="tdc">10900</td> + </tr><tr> +<td class="tdl">\(\alpha\)</td> +<td class="tdc">Aql(\(A_5\))</td> +<td class="tdc"></td> +<td class="tdc"> 8000</td> +<td class="tdc"></td> +<td class="tdc"></td> + </tr><tr> +<td class="tdl">\(\delta\)</td> +<td class="tdc">Cas(\(A_5\))</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"> 9000</td> +<td class="tdc">10700</td> + </tr><tr> +<td class="tdl">\(\alpha\)</td> +<td class="tdc">\(CM_i\)(\(F_5\))</td> +<td class="tdc"></td> +<td class="tdc"> 6000</td> +<td class="tdc"></td> +<td class="tdc"> 8300</td> + </tr><tr> +<td class="tdl">\(\alpha\)</td> +<td class="tdc">Aur(\(G_0\))</td> +<td class="tdc"> 5800</td> +<td class="tdc"> 6000</td> +<td class="tdc">5500-6000</td> +<td class="tdc"> 5500 <a href="#i">*</a></td> + </tr><tr> +<td class="tdl">\(\alpha\)</td> +<td class="tdc">\(B_{00}\)(\(K_0\))</td> +<td class="tdc"></td> +<td class="tdc"> 4000</td> +<td class="tdc"></td> +<td class="tdc"> 4200</td> + </tr><tr> +<td class="tdl">\(\beta\)</td> +<td class="tdc">Gem(\(K_0\))</td> +<td class="tdc"></td> +<td class="tdc"> 5500</td> +<td class="tdc">5000-5500</td> +<td class="tdc"> 4200</td> + </tr><tr> +<td class="tdl">\(\alpha\)</td> +<td class="tdc">Tau(\(K_5\))</td> +<td class="tdc"> 3000</td> +<td class="tdc"> 3500</td> +<td class="tdc"></td> +<td class="tdc"> 3400</td> + </tr><tr> +<td class="tdl">\(\alpha\)</td> +<td class="tdc">Ori(\(M_a\))</td> +<td class="tdc"> 2600</td> +<td class="tdc"> 3000</td> +<td class="tdc"></td> +<td class="tdc"> 3400</td> + </tr><tr> +<td class="tdl">\(\beta\)</td> +<td class="tdc">Peg(\(M_b\))</td> +<td class="tdc"> 2850</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"> 3200</td> + </tr> + </tbody> +</table> + +<p class="nindc"><a id="i">*</a> Temperature assumed in calibration of scale.</p> + + +<p>It was mentioned at the outset that dwarf stars appear to be at +a higher temperature than giants of the same spectral class. The +following table summarizes the differences in temperature, as compiled +by Seares.<a id="FNanchor_56" href="#Footnote_56" class="fnanchor">[56]</a></p> + +<h2><a id="TABLE_VII">TABLE VII</a></h2> + +<table class="autotable"> +<thead><tr> +<th class="tdc_bot" rowspan="2">Class </th> +<th class="tdc_top" colspan="2">Effective Temperature</th> +</tr><tr> +<th class="tdc_bot">Giant</th> +<th class="tdc_bot">Dwarf</th> +</tr> +</thead> +<tbody><tr> +<td class="tdc">\(F_5\)</td> +<td class="tdc">6080°</td> +<td class="tdc">6080°</td> +</tr><tr> +<td class="tdc">\(G_0\)</td> +<td class="tdc">5300 </td> +<td class="tdc">5770 </td> +</tr><tr> +<td class="tdc">\(G_5\)</td> +<td class="tdc">4610 </td> +<td class="tdc">5500 </td> +</tr><tr> +<td class="tdc">\(K_0\)</td> +<td class="tdc">3860 </td> +<td class="tdc">4880 </td> +</tr><tr> +<td class="tdc">\(K_5\)</td> +<td class="tdc">3270 </td> +<td class="tdc">4120 </td> +</tr><tr> +<td class="tdc">\(M_a\)</td> +<td class="tdc">3080 </td> +<td class="tdc">3330 </td> +</tr> +</tbody> +</table> + +<p><span class="pagenum" id="Page_32">[Pg 32]</span></p> + +<p>A more detailed list of giant and dwarf temperatures was compiled +in 1922 by Hertzsprung<a id="FNanchor_57" href="#Footnote_57" class="fnanchor">[57]</a> from all the material then available. +The tabulation that follows contains his values for \(c_2/T\) +(the “reciprocal temperature,” where \(c_2\) is 14,600), and the +corresponding absolute temperature, in degrees centigrade.</p> + +<h2><a id="TABLE_VIII">TABLE VIII</a></h2> + +<table class="autotable"> +<thead><tr> +<th class="tdc bb bt2 br">Mt. W. Class</th> +<th class="tdc bb bt2 br">\(c_2/T\) Giant</th> +<th class="tdc bb bt2 br">\(c_2/T\) Dwarf</th> +<th class="tdc bb bt2 br">Temperature<br> +Giant</th> +<th class="tdc bb bt2">Temperature<br> +Dwarf</th> +</tr> +</thead> +<tbody><tr> +<td class="tdc br">\(A_5\)</td> +<td class="tdc br"></td> +<td class="tdc br">2.00</td> +<td class="tdc br"></td> +<td class="tdc">7300°</td> +</tr><tr> +<td class="tdc br">\(A_6\)</td> +<td class="tdc br"></td> +<td class="tdc br">2.16</td> +<td class="tdc br"></td> +<td class="tdc">6770 </td> +</tr><tr> +<td class="tdc br">\(A_7\)</td> +<td class="tdc br"></td> +<td class="tdc br">2.08</td> +<td class="tdc br"></td> +<td class="tdc">6990 </td> +</tr><tr> +<td class="tdc br">\(A_8\)</td> +<td class="tdc br"></td> +<td class="tdc br">2.26</td> +<td class="tdc br"></td> +<td class="tdc">6460 </td> +</tr><tr> +<td class="tdc br">\(A_9\)</td> +<td class="tdc br"></td> +<td class="tdc br">2.30</td> +<td class="tdc br"></td> +<td class="tdc">6350 </td> +</tr><tr> +<td class="tdc br">\(F_0\)</td> +<td class="tdc br"></td> +<td class="tdc br">2.11</td> +<td class="tdc br"></td> +<td class="tdc">6920 </td> +</tr><tr> +<td class="tdc br">\(F_1\)</td> +<td class="tdc br"></td> +<td class="tdc br">2.30</td> +<td class="tdc br"></td> +<td class="tdc">6350 </td> +</tr><tr> +<td class="tdc br">\(F_2\)</td> +<td class="tdc br"></td> +<td class="tdc br">2.29</td> +<td class="tdc br"></td> +<td class="tdc">6370 </td> +</tr><tr> +<td class="tdc br">\(F_3\)</td> +<td class="tdc br"></td> +<td class="tdc br">2.34</td> +<td class="tdc br"></td> +<td class="tdc">6240 </td> +</tr><tr> +<td class="tdc br">\(F_4\)</td> +<td class="tdc br"></td> +<td class="tdc br">2.36</td> +<td class="tdc br"></td> +<td class="tdc">6190 </td> +</tr><tr> +<td class="tdc br">\(F_5\)</td> +<td class="tdc br"></td> +<td class="tdc br">2.48</td> +<td class="tdc br"></td> +<td class="tdc">5880 </td> +</tr><tr> +<td class="tdc br">\(F_6\)</td> +<td class="tdc br">2.30</td> +<td class="tdc br">2.51</td> +<td class="tdc br">6340°</td> +<td class="tdc">5810 </td> +</tr><tr> +<td class="tdc br">\(F_7\)</td> +<td class="tdc br"></td> +<td class="tdc br">2.45</td> +<td class="tdc br"></td> +<td class="tdc">5970 </td> +</tr><tr> +<td class="tdc br">\(F_8\)</td> +<td class="tdc br"></td> +<td class="tdc br">2.71</td> +<td class="tdc br"></td> +<td class="tdc">5100 </td> +</tr><tr> +<td class="tdc br">\(F_9\)</td> +<td class="tdc br">2.83</td> +<td class="tdc br">2.62</td> +<td class="tdc br">5170 </td> +<td class="tdc">5580 </td> +</tr><tr> +<td class="tdc br">\(G_0\)</td> +<td class="tdc br">2.92</td> +<td class="tdc br">2.68</td> +<td class="tdc br">5020 </td> +<td class="tdc">5440 </td> +</tr><tr> +<td class="tdc br">\(G_1\)</td> +<td class="tdc br">2.92</td> +<td class="tdc br">2.64</td> +<td class="tdc br">5020 </td> +<td class="tdc">5530 </td> +</tr><tr> +<td class="tdc br">\(G_2\)</td> +<td class="tdc br">3.15</td> +<td class="tdc br"></td> +<td class="tdc br">4730 </td> +<td class="tdc"></td> +</tr><tr> +<td class="tdc br">\(G_3\)</td> +<td class="tdc br">3.09</td> +<td class="tdc br"></td> +<td class="tdc br">4820 </td> +<td class="tdc"></td> +</tr><tr> +<td class="tdc br">\(G_4\)</td> +<td class="tdc br">3.15</td> +<td class="tdc br"></td> +<td class="tdc br">4730 </td> +<td class="tdc"></td> +</tr><tr> +<td class="tdc br">\(G_5\)</td> +<td class="tdc br">3.25</td> +<td class="tdc br">2.76</td> +<td class="tdc br">4480 </td> +<td class="tdc">5300 </td> +</tr><tr> +<td class="tdc br">\(G_6\)</td> +<td class="tdc br">3.20</td> +<td class="tdc br"></td> +<td class="tdc br">4560 </td> +<td class="tdc"></td> +</tr><tr> +<td class="tdc br">\(G_7\)</td> +<td class="tdc br">3.29</td> +<td class="tdc br"></td> +<td class="tdc br">4430 </td> +<td class="tdc"></td> +</tr><tr> +<td class="tdc br">\(G_8\)</td> +<td class="tdc br">3.39</td> +<td class="tdc br">3.03</td> +<td class="tdc br">4300 </td> +<td class="tdc">4840 </td> +</tr><tr> +<td class="tdc br">\(G_9\)</td> +<td class="tdc br">3.48</td> +<td class="tdc br">3.11</td> +<td class="tdc br">4180 </td> +<td class="tdc">4700 </td> +</tr><tr> +<td class="tdc br">\(K_0\)</td> +<td class="tdc br">3.50</td> +<td class="tdc br">3.05</td> +<td class="tdc br">4160 </td> +<td class="tdc">4790 </td> +</tr><tr> +<td class="tdc br">\(K_1\)</td> +<td class="tdc br">3.54</td> +<td class="tdc br"></td> +<td class="tdc br">4130 </td> +<td class="tdc"></td> +</tr><tr> +<td class="tdc br">\(K_2\)</td> +<td class="tdc br">3.83</td> +<td class="tdc br"></td> +<td class="tdc br">3810 </td> +<td class="tdc"></td> +</tr><tr> +<td class="tdc br">\(K_3\)</td> +<td class="tdc br">3.86</td> +<td class="tdc br"></td> +<td class="tdc br">3870 </td> +<td class="tdc"></td> +</tr><tr> +<td class="tdc br">\(K_4\)</td> +<td class="tdc br">4.14</td> +<td class="tdc br"></td> +<td class="tdc br">3530 </td> +<td class="tdc"></td> +</tr><tr> +<td class="tdc br">\(K_5\)</td> +<td class="tdc br">4.33</td> +<td class="tdc br"></td> +<td class="tdc br">3370 </td> +<td class="tdc"></td> +</tr><tr> +<td class="tdc br">\(K_6\)</td> +<td class="tdc br">4.36</td> +<td class="tdc br"></td> +<td class="tdc br">3350 </td> +<td class="tdc"></td> +</tr><tr> +<td class="tdc br">\(K_8\)</td> +<td class="tdc br">4.35</td> +<td class="tdc br"></td> +<td class="tdc br">3360 </td> +<td class="tdc"></td> +</tr><tr> +<td class="tdc br">\(M_a\)</td> +<td class="tdc br">4.49</td> +<td class="tdc br"></td> +<td class="tdc br">3250 </td> +<td class="tdc"></td> +</tr><tr> +<td class="tdc br">\(M_b\)</td> +<td class="tdc br">4.45</td> +<td class="tdc br"></td> +<td class="tdc br">3280 </td> +<td class="tdc"></td> +</tr><tr> +<td class="tdc bb br">\(M_c\)</td> +<td class="tdc bb br">3.93</td> +<td class="tdc bb br"></td> +<td class="tdc bb br">3720 </td> +<td class="tdc bb"></td> + </tr> + </tbody> +</table> + +<p><span class="pagenum" id="Page_33">[Pg 33]</span></p> + +<p>The difference in temperature between giant and dwarf stars of the same +spectral class is clearly shown in the foregoing tables. The relation +of absolute magnitude to effective temperature within a given class +must be regarded as definitely established by observation.</p> + +<p>The temperatures for the cooler giant stars in both these lists are +somewhat lower than those given for the corresponding classes in <a href="#TABLE_V">Table V</a>. +The temperature of \(K_0\), for instance, is placed nearer to 4000° +than to 4500°. The fact that the sun, a typical \(G_0\) dwarf, has an +effective temperature of 5600° seems to favor these lower values.</p> + +<h2><a id="TABLE_IX">TABLE IX</a></h2> + +<table class="autotable"> +<thead><tr> +<th class="tdc">Class</th> +<th class="tdc">Temperature</th> +<th class="tdc">Class</th> +<th class="tdc">Temperature</th> +</tr> +</thead> +<tbody><tr> +<td class="tdc">\(M_a\)</td> +<td class="tdc">3000°</td> +<td class="tdc">\(A_3\)</td> +<td class="tdc">9000°</td> + </tr><tr> +<td class="tdc">\(K_5\)</td> +<td class="tdc">3000 </td> +<td class="tdc">\(A_0\)</td> +<td class="tdc">10000 </td> + </tr><tr> +<td class="tdc">\(K_2\)</td> +<td class="tdc">3500 </td> +<td class="tdc">\(B_8\)</td> +<td class="tdc">13500 </td> + </tr><tr> +<td class="tdc">\(K_0\)</td> +<td class="tdc">4000 </td> +<td class="tdc">\(B_5\)</td> +<td class="tdc">15000 </td> + </tr><tr> +<td class="tdc">\(G_5\)</td> +<td class="tdc">5000 </td> +<td class="tdc">\(B_3\)</td> +<td class="tdc">17000 </td> + </tr><tr> +<td class="tdc">\(G_0\)</td> +<td class="tdc">5600 </td> +<td class="tdc">\(B_{1.5}\)</td> +<td class="tdc">18000 </td> + </tr><tr> +<td class="tdc">\(F_5\)</td> +<td class="tdc">7000 </td> +<td class="tdc">\(B_0\)</td> +<td class="tdc">20000 </td> + </tr><tr> +<td class="tdc">\(F_0\)</td> +<td class="tdc">7500 </td> +<td class="tdc">\(O\)</td> +<td class="tdc">25000 </td> + </tr><tr> +<td class="tdc">\(A_5\)</td> +<td class="tdc">8400 </td> +<td class="tdc"></td> +<td class="tdc">35000 </td> +</tr> + </tbody> +</table> + +<p>In concluding the summary of stellar temperatures, the ionization +temperature scale is given in the foregoing table. The discussion on +which the table is based is contained in <a href="#CHAPTER_VI">Chapters VI</a> to <a href="#CHAPTER_V">IX</a>, and it is +merely placed here for comparison with the preceding tabulations.</p> + + +<div class="footnotes"><h3>FOOTNOTES:</h3> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_43" href="#FNanchor_43" class="label">[43]</a> +Eddington, Zeit. f. Phys., 7, 351, 1921.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_44" href="#FNanchor_44" class="label">[44]</a> +Phil. Trans., 223A, 201, 1922.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_45" href="#FNanchor_45" class="label">[45]</a> +Chapter IX, <a href="#Page_136">p. 136</a>.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_46" href="#FNanchor_46" class="label">[46]</a> +Chapter XIV, <a href="#Page_195">p. 195</a>.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_47" href="#FNanchor_47" class="label">[47]</a> +Wilsing and Scheiner, Pots. Pub., 24, No. 74, 1919.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_48" href="#FNanchor_48" class="label">[48]</a> +Pots. Pub., 24, No. 76, 1920.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_49" href="#FNanchor_49" class="label">[49]</a> +H. A., 76, 107, 1916.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_50" href="#FNanchor_50" class="label">[50]</a> +A.N., 193, 356, 1912.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_51" href="#FNanchor_51" class="label">[51]</a> +A. N., 218, 210, 1923; <i>ibid.</i>, 219, 22 and 354, +1923; Die Strahlung der Sterne, Berlin, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_52" href="#FNanchor_52" class="label">[52]</a> +Rep., Smithsonian Ap. Obs., 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_53" href="#FNanchor_53" class="label">[53]</a> +Pop. Ast., 21, 105, 1923.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_54" href="#FNanchor_54" class="label">[54]</a> +M. N. R. A. S., 85, 212, 1925.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_55" href="#FNanchor_55" class="label">[55]</a> +Pub. Dom. Ap. Obs., 2, 12, 1923.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_56" href="#FNanchor_56" class="label">[56]</a> +Ap. J., 55, 202, 1922.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_57" href="#FNanchor_57" class="label">[57]</a> +Lei. An., 14, 1, 1922.</p> + +</div> +</div> + +<hr class="chap x-ebookmaker-drop"> + +<div class="chapter"> +<p><span class="pagenum" id="Page_34">[Pg 34]</span></p> + +<h2 class="nobreak" id="CHAPTER_III">CHAPTER III<br> +PRESSURES IN STELLAR ATMOSPHERES</h2> +</div> + + +<p class="nind"> +THE theory of thermal ionization enables us to make an analysis of the +spectrum of the stellar reversing layer by predicting the number of +atoms of any given kind that will be effective in absorbing light from +the interior of the star, under given conditions, and by comparing the +predicted values with the observed intensities of the corresponding +absorption lines. The results depend partly on definite physical +constants associated with the atoms—the ionization and excitation +potentials, and the arrangement of the electrons around the nucleus. +The temperature and pressure of the region in which the atom is +situated are also required before the theory can be applied. The scale +of stellar temperatures was discussed in the preceding chapter, and +the present chapter is devoted to a synopsis of the modern views as to +pressures in the reversing layer.</p> + +<p>Strictly speaking, we cannot refer to “the pressure in the reversing +layer,” for, like the temperature, the pressure has a gradient +throughout the star. This gradient, as derived from the theory of +radiative equilibrium,<a id="FNanchor_58" href="#Footnote_58" class="fnanchor">[58]</a> is steep in the far interior of the +star, but towards the outside the rapid fall of pressure begins to +decrease, and changes somewhat abruptly to a very small gradient in +the photospheric region, where radiation pressure and gravitation +are of the same order of magnitude. Outside this layer of transition +between the region dominated by radiation pressure and the region +dominated by gravitation, the pressure gradient is very shallow, and +decreases until, in the tenuous outer regions of the star, there is +no appreciable pressure gradient, and atoms are practically floating +freely.</p> + +<p><span class="pagenum" id="Page_35">[Pg 35]</span></p> + +<p>The outermost regions of the atmosphere, at these exceedingly low +pressures, make little or no contribution to the ordinary stellar +spectrum; they can only be studied in the high-level chromosphere by +means of the flash spectrum obtained at a total eclipse of the sun. +The spectra that are ordinarily examined are from a region that is +at an appreciable depth within the star—the depth from which the +light of each individual wave-length can penetrate. The “layer” of +which we can obtain a spectrum is therefore not at the same depth +for all frequencies; it is most deep-seated in regions of continuous +background, and nearest to the surface of the star at the centers +of strong absorption lines. The pressures from which the different +parts of the spectrum originate differ in the same way, and the idea +of “pressure in the reversing layer” is not an easy one to define +significantly.</p> + +<p>For theoretical purposes it is usual to deal with the pressure at +a given “optical depth” (a measure of the <i>amount of absorbing +matter</i> traversed by the radiation in coming from the level +considered). The optical depth \(\tau\) is connected with the density +\(\rho\), the mass coefficient of absorption for unit density, \(k\), +and the vertical depth, \(z\), in the star, by the relation<a id="FNanchor_59" href="#Footnote_59" class="fnanchor">[59]</a></p> + +<p>\[ +k\rho\, dz = d \tau +\] +The density gradient is thus eliminated. The optical depth is +furthermore related to the pressure \(p\) by the relations +\[ +dp/dz = g \rho +\] +where \(g\) is the value of gravity at the point in question, and +\[ +dp/d \tau = g/k +\] +whence +\[ +p = (g/k) \tau +\]</p> + +<p>In considering the stellar atmosphere we are dealing with a layer +so near the surface that the value of g involved is effectively the +“surface gravity” for the star. If \(k\) is constant, a condition +<span class="pagenum" id="Page_36">[Pg 36]</span> +probably approximately fulfilled,<a id="FNanchor_60" href="#Footnote_60" class="fnanchor">[60]</a> the pressure at constant optical +depth is then directly proportional to the surface gravity, which +varies as the product of the mean density and the radius of the star. +Some idea of the range in pressure with which we shall be concerned in +the stellar atmosphere can therefore be obtained from stars of known +mean density and radius.</p> + +<p>The data for eight such stars, all of the second type, are contained +in <a href="#TABLE_X">Table X</a>, which is adapted from tabulations given by Shapley.<a id="FNanchor_61" href="#Footnote_61" class="fnanchor">[61]</a> +Successive columns contain the name of the star, the spectral class, +the mean densities of the two components in terms of the solar density, +the hypothetical radii of the two components (on the assumption of +solar mass) in terms of the sun’s radius, and the product of mean +density and radius for each component.</p> + +<h2><a id="TABLE_X">TABLE X</a></h2> + +<table class="autotable"> +<thead><tr> +<th class="tdc bb bt2 br" colspan="2">Star</th> +<th class="tdc bb bt2 br"> Class </th> +<th class="tdc bb bt2 br" colspan="2"> Mean density </th> +<th class="tdc bb bt2 br" colspan="2"> Radius </th> +<th class="tdc bb bt2" colspan="2"> Product </th> +</tr> +</thead> +<tbody><tr> +<td class="tdl">SX</td> +<td class="tdr br">Cas</td> +<td class="tdc br">\(G_3\)</td> +<td class="tdl">0.0004</td> +<td class="tdl br">0.0002</td> +<td class="tdl">15.3</td> +<td class="tdl br">18.6</td> +<td class="tdl">0.006</td> +<td class="tdl">0.004</td> +</tr><tr> +<td class="tdl">RX</td> +<td class="tdr br">Cas</td> +<td class="tdc br">\(K_0\)</td> +<td class="tdl">0.0005</td> +<td class="tdl br">0.0004</td> +<td class="tdl">14.3</td> +<td class="tdl br">14.3</td> +<td class="tdl">0.007</td> +<td class="tdl">0.006</td> +</tr><tr> +<td class="tdl">RZ</td> +<td class="tdr br">Oph</td> +<td class="tdc br">\(F_8\)</td> +<td class="tdl">0.001</td> +<td class="tdl br">0.00003</td> +<td class="tdl">10.1</td> +<td class="tdl br">33.5</td> +<td class="tdl">0.010</td> +<td class="tdl">0.001</td> +</tr><tr> +<td class="tdl">RT</td> +<td class="tdr br">Lac</td> +<td class="tdc br">\(G_5\)</td> +<td class="tdl">0.0013</td> +<td class="tdl br">0.010</td> +<td class="tdl"> 4.6</td> +<td class="tdl br"> 4.6</td> +<td class="tdl">0.059</td> +<td class="tdl">0.046</td> +</tr><tr> +<td class="tdl">W</td> +<td class="tdr br">Cru</td> +<td class="tdc br">\(G_p\)</td> +<td class="tdl">0.00002</td> +<td class="tdl br">0.000025</td> +<td class="tdl">94</td> +<td class="tdl br">36</td> +<td class="tdl">0.00019</td> +<td class="tdl">0.0009</td> +</tr><tr> +<td class="tdl">U</td> +<td class="tdr br">Peg</td> +<td class="tdc br">\(F_3\)</td> +<td class="tdl">0.83</td> +<td class="tdl br">0.67</td> +<td class="tdl"> 1.2</td> +<td class="tdl br"> 1.2</td> +<td class="tdl">1.0</td> +<td class="tdl">0.8</td> +</tr><tr> +<td class="tdl">W</td> +<td class="tdr br">\(UM_a\)</td> +<td class="tdc br">G</td> +<td class="tdl">1.8</td> +<td class="tdl br">1.8</td> +<td class="tdl"> 0.9</td> +<td class="tdl br"> 0.9</td> +<td class="tdl">1.6</td> +<td class="tdl">1.6</td> +</tr><tr> +<td class="tdl bb">Sun</td> +<td class="tdr bb br"></td> +<td class="tdc bb br">\(G_0\)</td> +<td class="tdl bb">1.0</td> +<td class="tdr bb br"></td> +<td class="tdl bb"> 1.0</td> +<td class="tdl bb br"></td> +<td class="tdl bb">1.0</td> +<td class="tdl bb"></td> +</tr> + </tbody> +</table> + +<p>In mean density these stars display a range of \(10^{6}\), while the +range in surface gravity is \(10^{4}\), illustrating the significant fact +that the mean density varies far more widely than the surface gravity. +The latter quantity is the important one in determining the pressure +that may be assumed to exist in the reversing layer. If the masses of +the very luminous stars of low mean density, such as W Crucis, exceed +the solar mass, as they most probably do, the hypothetical radii are +<span class="pagenum" id="Page_37">[Pg 37]</span> +increased, and the range in surface gravity becomes even smaller than +before.</p> + +<p>The data for stars of known mean density and radius permit the +estimation of the range in surface gravity, and hence of the range +in pressure, encountered in the reversing layer. In the absence of +knowledge of the appropriate optical depth, however, the <i>actual</i> +pressure cannot be deduced from such considerations, and recourse +must be made to more indirect methods. The present view is based upon +a number of considerations, none of which would alone be of great +weight. All of the conclusions, taken together, however, indicate +that the upper limit of the pressure for the region in which the +Fraunhofer lines originate is of the order of +\(\displaystyle{10^{4}\, \text{atmospheres}}\).</p> + +<p>Attention was first called to the probability of an extremely low +pressure in the reversing layer by R. H. Fowler and Milne,<a id="FNanchor_62" href="#Footnote_62" class="fnanchor">[62]</a> in +advancing the form of ionization theory which is to be analyzed in +later chapters. The conclusion that the pressure in the reversing layer +is exceedingly low was a direct outcome of their discussion, and they +mentioned that the results from other methods converged in the same +direction.</p> + +<p>Russell and Stewart,<a id="FNanchor_63" href="#Footnote_63" class="fnanchor">[63]</a> in a specific discussion of the pressures +at the surface of the sun, have established beyond question, and on +quite other grounds, that the pressure for the solar reversing layer +is indeed of the order suggested by Fowler and Milne. The value +\(\displaystyle{10^{4}\, \text{atmospheres}}\) need then no longer be +regarded as a <i>result</i> of the Fowler-Milne theory, and may be used +without redundancy in deriving a stellar temperature scale from that +theory.</p> + + +<p class="nindc space-above2"> +METHODS OF ESTIMATING REVERSING LAYER PRESSURES</p> + + +<p>Russell and Stewart examined the evidence for reversing layer pressures +derived from the following sources: (<i>a</i>) Shifts of spectral lines +due to pressure, (<i>b</i>) Sharpness of lines, (<i>c</i>) Widths of +lines, (<i>d</i>) Flash spectrum, (<i>e</i>) Equilibrium of outer +layers, (<i>g</i>) Ionization and chemical equilibrium in the solar +<span class="pagenum" id="Page_38">[Pg 38]</span> +atmosphere. In addition to these we have (<i>f</i>) the observed limit +of the Balmer series in the hotter stars, where the hydrogen lines are +at or near their maximum. These sources of evidence will now be briefly +discussed.</p> + +<p>(a) <i>Shifts of Spectral Lines.</i>—It was at one time supposed that +displacements of spectral lines, corresponding to pressures of several +atmospheres, could be found in stellar spectra. More recent work,<a id="FNanchor_64" href="#Footnote_64" class="fnanchor">[64]</a> +however, has shown conclusively that the pressure shifts that occur are +so small that it is impossible to estimate a pressure from them with +any approach to accuracy. The estimated pressures are of the same order +as their probable errors. This being so, the most that can be expected +of the method based upon pressure effects is a demonstration of whether +or no the pressure exceeds 0.1 atmosphere, and this question has now +been satisfactorily answered in the negative.</p> + +<p><span class="pagenum" id="Page_39">[Pg 39]</span></p> + +<p>(b) <i>Sharpness of lines.</i>—The occurrence, as sharp distinct +lines in the spectra of the stellar atmosphere, of lines that are +diffuse in the laboratory at atmospheric pressure, and only become +sharp when the pressure is very much reduced, indicates that the +pressure in the reversing layer must be extremely low. The mere +existence of distinct hydrogen lines points to a pressure of less +than half an atmosphere, as was shown by Evershed,<a id="FNanchor_65" href="#Footnote_65" class="fnanchor">[65]</a> and the lines +4111, 4097, 3912 of chromium,<a id="FNanchor_66" href="#Footnote_66" class="fnanchor">[66]</a> 3421, 3183 of barium,<a id="FNanchor_67" href="#Footnote_67" class="fnanchor">[67]</a> and 4355, +4108, 3972 of calcium,<a id="FNanchor_68" href="#Footnote_68" class="fnanchor">[68]</a> which are sharp and distinct in the solar +spectrum, but which only lose their diffuseness in the laboratory +under vacuum conditions, indicates pressures probably far lower than +0.1 atmospheres. The lines of doubly ionized nitrogen, which are seen +as sharp clear absorption lines in the early \(B\) stars and the cooler +\(O\) stars,<a id="FNanchor_69" href="#Footnote_69" class="fnanchor">[69]</a> are also somewhat hazy under even the finest laboratory +conditions,<a id="FNanchor_70" href="#Footnote_70" class="fnanchor">[70]</a> and probably arise in regions of very low pressure in +the stellar atmosphere.</p> + +<p>(c) <i>Widths of lines.</i>—The width of an absorption line, produced +by “Rayleigh Scattering” close to resonance conditions, is given by +Stewart<a id="FNanchor_71" href="#Footnote_71" class="fnanchor">[71]</a> as +\[ +\Delta = (5.8 \times 10^{-18}) \lambda \surd{N} +\] +where \(\Delta\) is the observed width of the line, \(\lambda\) the +wave-length expressed in the same units, and \(N\) the number of +molecules per square centimeter column in the line of sight.</p> + +<p>It is unfortunate that the widths of Fraunhofer lines are hard to +measure and difficult to interpret. Results obtained from objective +prism spectra will probably differ from those derived with the aid of +a slit spectrograph, and moreover, in estimating a line with wings it +is hard to judge what should be regarded as the “true” line width. +Russell and Stewart<a id="FNanchor_72" href="#Footnote_72" class="fnanchor">[72]</a> estimate \(\displaystyle{\Delta / \lambda = +10^{-4}}\) for the \(D\) lines in the solar spectrum. Then, on the +assumption that the reversing layer has a thickness of a hundred +kilometers, the partial pressure of neutral sodium in the reversing +layer, as derived by Russell and Stewart from the formula just quoted, +is of the order \(\displaystyle{10^{-9}\, \text{atmospheres}}\). At +the solar temperature, 5600°, about 99 per cent of the sodium present +is in the ionized condition,<a id="FNanchor_73" href="#Footnote_73" class="fnanchor">[73]</a> and thus the total partial pressure +of sodium atoms may be of the order \(10^{-7}\, \text{atmospheres}\). +If it be assumed that sodium constitutes about 5 per cent of the total +material present, the <i>total</i> pressure thus derived is of the +order \(\displaystyle{10^{-6}\, \text{atmospheres}}\).</p> + +<p><span class="pagenum" id="Page_40">[Pg 40]</span></p> + +<p>The \(D\) lines are of course the ultimate lines of neutral sodium. +It will be shown<a id="FNanchor_74" href="#Footnote_74" class="fnanchor">[74]</a> in <a href="#CHAPTER_IX">Chapter IX</a> that the partial electron pressure +in the region from which ultimate lines originate is probably between +\(\displaystyle{10^{-9}\, \text{and}\, 10^{-10}\,\text{atmospheres}}\) +at maximum. When 99 per cent of the atoms are ionized, the +pressure rises by a factor of about 100, and the corresponding +partial electron pressure becomes between +\(\displaystyle{10^{-7}\, \text{and}\, 10^{-8}\,\text{atmospheres}}\). +As the total pressure is probably, at the solar temperature, about +twice the partial electron pressure, the total pressure should be nearer +to \(\displaystyle{10^{-7}\,\text{atmospheres}}\).</p> + +<p>The total pressure derived in <a href="#CHAPTER_IX">Chapter IX</a> is the pressure corresponding +to the median frequency of the sodium atoms that send out light to +the exterior—it may be regarded as the average pressure for the +visible sodium. The total pressure derived from the line width, on +the other hand, is the pressure at the bottom of the layer of visible +sodium, and might therefore be expected slightly to exceed the average +pressure for the visible sodium atoms. The difference encountered, +partial electron pressure, the total pressure should be nearer to +\(\displaystyle{10^{-7}\, \text{atmospheres}}\) for the average +pressure, and partial electron pressure, the total pressure should be +nearer to \(\displaystyle{10^{-6}\, \text{atmospheres}}\) for the total +absorption pressure, is in the direction that would be anticipated, +although it is larger than might have been expected. Neither value +is, however, of very high accuracy, and probably the agreement can be +regarded as quite satisfactory.</p> + +<p>If the same formula be applied to the hydrogen lines, which may have a +width<a id="FNanchor_75" href="#Footnote_75" class="fnanchor">[75]</a> of the order of 5Å, high values for the partial pressure of +hydrogen are obtained. The behavior of hydrogen in the spectra of the +cooler stars,<a id="FNanchor_76" href="#Footnote_76" class="fnanchor">[76]</a> and the abnormally high abundance<a id="FNanchor_77" href="#Footnote_77" class="fnanchor">[77]</a> derived for it +in <a href="#CHAPTER_XIII">Chapter XIII</a>, suggest that here, again, a definite abnormality of +the behavior of hydrogen is involved.</p> + +<p>(d) <i>Flash Spectrum.</i>—It was pointed out by Russell and +Stewart<a id="FNanchor_78" href="#Footnote_78" class="fnanchor">[78]</a> that the density in the region that gives the flash +spectrum must be exceedingly low. If this were not the case, the +intensity of the scattered sunlight would be great enough, as +compared to the flash itself, to register on the plate as continuous +background in the time required to photograph the flash. The pressure +thus estimated, from the minimum amount of material required to give +scattered sunlight strong enough to be registered, is less than +\(\displaystyle{2 \times 10^{-5}\, \text{atmospheres}}\).</p> + +<p>(e) <i>Radiative Equilibrium of the Outer Layers.</i>—At the edge of a +star, where radiation pressure and gravitation no longer balance, and +in consequence the existence of temperature and pressure gradients, +<span class="pagenum" id="Page_41">[Pg 41]</span> +such as we observe in the reversing layer, becomes possible, the +equations given by Eddington<a id="FNanchor_79" href="#Footnote_79" class="fnanchor">[79]</a> for the equilibrium of the interior no +longer hold. The outer layers fall off more steeply than the equations +predict, and in consequence it is not possible to use the equations in +deriving values for the pressure or density corresponding to a layer +near the boundary at a given temperature. It is certain, however, that +the density deduced from the equations will be far too <i>high</i>, and +so the predicted density at a given temperature may be used to indicate +that the pressures at the boundary of a giant star are indeed very low.</p> + +<p>The following table is adapted from the one given by Eddington for the +relation between distance, \(r\), from the center, density \(d\), and +temperature \(T\), for a typical giant star of Class \(F_7\), effective +temperature 6500°. The distance from the center is expressed in terms +of the solar radius, the density in grams per cubic centimeter, and +the temperature in absolute units. The last entry in the first column +represents the total radius of the star.</p> + +<table class="autotable"> +<thead><tr> +<th class="tdc">\(r\) </th> +<th class="tdc"> \(d\) </th> +<th class="tdc"> \(T\) </th> +<th class="tdc"> \(r\) </th> +<th class="tdc"> \(d\) </th> +<th class="tdc"> \(T\)</th> +</tr> +</thead> +<tbody><tr> +<td class="tdc">0</td> +<td class="tdc">0.1085</td> +<td class="tdc">6,590,000°</td> +<td class="tdc">4</td> +<td class="tdl">0.0010</td> +<td class="tdr">1,380,000°</td> + </tr><tr> +<td class="tdc">1</td> +<td class="tdc">0.0678</td> +<td class="tdc">5,640,000 </td> +<td class="tdc">5</td> +<td class="tdl">0.00015</td> +<td class="tdr">730,000 </td> + </tr><tr> +<td class="tdc">2</td> +<td class="tdc">0.0215</td> +<td class="tdc">3,840,000 </td> +<td class="tdc">6</td> +<td class="tdl">0.0000093</td> +<td class="tdr">290,000 </td> + </tr><tr> +<td class="tdc">3</td> +<td class="tdc">0.0050</td> +<td class="tdc">2,370,000 </td> +<td class="tdc">6.9</td> +<td class="tdl">0.000000</td> +<td class="tdr">...... </td> + </tr> + </tbody> +</table> + +<p>At a depth where the temperature is 290,000°, ten times the temperature +in the reversing layer of any known star, the density given is about +\(\displaystyle{10^{-5}\, \text{grams per cubic centimeter}}\). An +atmosphere a hundred kilometers in thickness (the supposed approximate +depth of the reversing layer) and of this density would contain only +a hundred grams per square centimeter of surface. In order to bring +the density into harmony with the densities derived for the reversing +layer it is necessary to suppose that the value<a id="FNanchor_80" href="#Footnote_80" class="fnanchor">[80]</a> of \(d\) falls to 0.4 +per cent of its value at 290,000° as the temperature falls, from +<span class="pagenum" id="Page_42">[Pg 42]</span> +290,000° to 29,000°, to 10 per cent of its value. The fall of density +displayed in the table appears to be rapid enough to warrant this +supposition; and in any case, as was pointed out earlier, the actual +fall is probably greater than the formula predicts. The general theory +of stellar equilibrium is, then, consistent with very low pressures in +the reversing layer. More than this cannot be said, as the formulae are +not directly applicable.</p> + +<p>(f) <i>Observed Limit of the Balmer Series.</i>—The earlier members of +the Balmer series of hydrogen are produced by the transfer of electrons +from 2-quantum orbits to 3-quantum orbits (\(H \alpha\)), 4-quantum +orbits (\(H \beta\)), and so forth. The later members of the series +are associated with orbits of higher and higher quantum numbers. The +major axis of the orbit varies as the square of the quantum number, and +therefore a hydrogen atom which is producing, say, \(H \omega\), is +effectively much larger than one which is giving rise to \(H \alpha\). +As was early suggested by Bohr,<a id="FNanchor_81" href="#Footnote_81" class="fnanchor">[81]</a> the production of the higher +members of the series must depend upon the possibility of existence of +the corresponding outer orbits. As a preliminary assumption it appears +probable that the existence of the larger orbits will depend on the +proximity of neighboring atoms, and hence on the pressure.</p> + +<p>The theoretical questions involved are very complex, and the present +discussion is merely tentative. When the idea that the maximum number +of lines that could be produced was a function of the pressure was +first set forth, the available laboratory evidence appeared all to be +in its favor. The maximum number of Balmer lines that had been produced +in the vacuum tube was five, while it was well known that over twenty +could be traced in absorption in some stellar atmospheres. Since that +time, however, the work of R. W. Wood<a id="FNanchor_82" href="#Footnote_82" class="fnanchor">[82]</a> has produced forty-seven +lines of the Balmer absorption series of sodium in the laboratory at +considerable pressures, and evidently the simple theory, relying on the +mutual distances of the atoms to determine the number of lines that +<span class="pagenum" id="Page_43">[Pg 43]</span> +can be produced, cannot be applied in this case. The matter has been +discussed by Franck,<a id="FNanchor_83" href="#Footnote_83" class="fnanchor">[83]</a> who points out that the outermost effective +orbit in the sodium atom that gives the forty-seventh line must embrace +large numbers of other atoms. He suggests that <i>collisions</i> are +chiefly responsible for the production of the absorption lines.</p> + +<p>Even though the simple theory is inapplicable to the laboratory +conditions, it is not necessarily invalid in the stellar atmosphere, +where conditions are far more simple, and where, in particular, the +effects of collisions are negligible. There appears, moreover, to be +a distinct observational correlation between the pressure and the +number of observable hydrogen lines. The importance of the wave-length +of the beginning of the continuous absorption, which lies just to the +red of the last Balmer line observed, and extends toward the violet, +was first indicated by Wright,<a id="FNanchor_84" href="#Footnote_84" class="fnanchor">[84]</a> who recorded that the absorption +head was farther to the red in \(\alpha\) Lyrae than in \(\alpha\) +Cygni. This fact is obviously reflated to the difference in pressure +in the atmospheres of the two stars, one of which is a normal \(A\) star, +while the other is a super-giant. The observational and theoretical +importance of the question has also been discussed by Saha,<a id="FNanchor_85" href="#Footnote_85" class="fnanchor">[85]</a> and by +Nicholson.<a id="FNanchor_86" href="#Footnote_86" class="fnanchor">[86]</a></p> + +<p>The observational data in the hands of the writers just quoted were +very meagre, and the present writer and Miss Howe<a id="FNanchor_87" href="#Footnote_87" class="fnanchor">[87]</a> have recently +attempted to obtain information on the number of observed Balmer +lines in a large number of stars, and to examine the correlation with +absolute magnitude. A distinct correlation is found between the number +of lines observed and the reduced proper motion, which is chosen as the +best available criterion of absolute magnitude for the numerous stars +involved (Class \(A\) brighter than the fifth magnitude). It therefore +appears that the pressure, and hence the proximity of the atoms, has +some influence upon the possibility of the production of a line. The +<span class="pagenum" id="Page_44">[Pg 44]</span> +application of Bohr’s original suggestion is hence of considerable +interest, and the resulting pressures may profitably be compared with +the pressures otherwise derived for the reversing layer.</p> + +<p>The maximum number of lines seen, while quite consistent for plates +made with the <i>same</i> dispersion, is somewhat increased when the +dispersion is made much greater. The number of lines seen in the +spectra of various stars with strong hydrogen lines, made with a +dispersion of about 40 mm. between \(H \beta\) and \(H \epsilon\), +varies between thirteen and twenty. The corresponding pressures, +derived from Bohr’s estimate that a pressure of about 0.02 mm. would be +required for the production of thirty-three Balmer lines, and +on the assumption that the pressure varies as the sixth power +of the quantum number, lie between \(10^{-3}\) and +\(\displaystyle{10^{-4}\,\text{atmospheres}}\). +These pressures are of course to be regarded as upper limits, for it +is possible to miss several lines at the violet end of the series, and +Wright, with larger dispersion, does indeed record twenty-four Balmer +lines in \(\alpha\) Cygni; on the other hand it is not likely that the +estimated number will exceed the actual number of lines.</p> + +<p>The pressures in the reversing layer, as derived from the observed +limit of the Balmer series, are then of the same order as the pressures +derived by the other methods outlined above. This is of especial +interest because the method, if applicable, is a direct one, and gives +results for individual stars, whereas all the other methods, excepting +the one based on pressure shifts, are essentially indirect.</p> + +<p>(g) <i>Ionization and Chemical Equilibrium.</i>—The evidence adduced +by Russell and Stewart<a id="FNanchor_88" href="#Footnote_88" class="fnanchor">[88]</a> has been greatly amplified by Fowler +and Milne,<a id="FNanchor_89" href="#Footnote_89" class="fnanchor">[89]</a> and by the data bearing on their theory which were +subsequently published by the writer<a id="FNanchor_90" href="#Footnote_90" class="fnanchor">[90]</a> and by Menzel.<a id="FNanchor_91" href="#Footnote_91" class="fnanchor">[91]</a> It is +not intended to present the evidence from ionization theory here in +<i>support</i> of the low pressures inferred by the other methods for +<span class="pagenum" id="Page_45">[Pg 45]</span> +the reversing layer. The pressure derived in the present chapter, and +considered as independently established, will be used in <a href="#CHAPTER_VII">Chapters VII</a> +ff. to derive a stellar temperature scale, for the reversing layer, +from the line-intensity data presented.</p> + + +<p class="nindc space-above2"> +SUMMARY</p> + + +<p>The following tabulation contains a synopsis of the reversing layer +pressures derived by the methods that have been outlined.</p> + +<p>The extreme tenuity of the stellar atmosphere appears to be +unquestionably established by the data set forth above, and a maximum +effective pressure of \(\displaystyle{10^{-4}\, \text{atmospheres}}\) +may therefore be assumed in a discussion of the spectra of reversing +layers.</p> + +<table class="autotable"> +<tbody><tr> +<td class="tdl">Pressure Shifts </td> +<td class="tdl"> less than \(10^{-1}\)</td> + </tr><tr> +<td class="tdl">Line Sharpness </td> +<td class="tdl"> less than \(10^{-1}\)</td> + </tr><tr> +<td class="tdl">Line Width </td> +<td class="tdl"> \(10^{-6}\)</td> + </tr><tr> +<td class="tdl">Flash Spectrum </td> +<td class="tdl"> \(2~\times~ 10^{-5}\)</td> + </tr><tr> +<td class="tdl">Radiative Equilibrium </td> +<td class="tdl"> order of \(10^{-4}\)</td> + </tr><tr> +<td class="tdl">Limit of Balmer Series </td> +<td class="tdl"> \(10^{-3}\) to \(10^{-4}\) (upper limit)</td> + </tr><tr> +<td class="tdl">(Ionization </td> +<td class="tdl"> \(10^{-4}\) to \(10^{-9}\))</td> + </tr> + </tbody> +</table> + +<div class="footnotes"><h3>FOOTNOTES:</h3> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_58" href="#FNanchor_58" class="label">[58]</a> +Eddington, Zeit. f. Phys., 7, 731, 1921.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_59" href="#FNanchor_59" class="label">[59]</a> +Pannekoek, B. A. N., 19, 1922.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_60" href="#FNanchor_60" class="label">[60]</a> +Milne, Phil. Mag., 47, 217, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_61" href="#FNanchor_61" class="label">[61]</a> +Ap. J., 42, 271, 1915; Princeton Contr. No. 3, 82, 1915.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_62" href="#FNanchor_62" class="label">[62]</a> +M. N. R. A. S., 83, 403, 1923.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_63" href="#FNanchor_63" class="label">[63]</a> +Ap. J., 59, 197, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_64" href="#FNanchor_64" class="label">[64]</a> +St. John and Babcock, Ap. J., 60, 32, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_65" href="#FNanchor_65" class="label">[65]</a> +M. N. R. A. S., 82, 394, 1922.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_66" href="#FNanchor_66" class="label">[66]</a> +King, Ap. J., 41, 110, 1915.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_67" href="#FNanchor_67" class="label">[67]</a> +King, Ap. J., 48, 32, 1918.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_68" href="#FNanchor_68" class="label">[68]</a> +Saunders, quoted by Russell and Stewart, Ap. J., 59, 197, +1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_69" href="#FNanchor_69" class="label">[69]</a> +Payne, H. C. 256, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_70" href="#FNanchor_70" class="label">[70]</a> +A. Fowler, M. N. R. A. S., 80, 692, 1920.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_71" href="#FNanchor_71" class="label">[71]</a> +Stewart, Ap. J., in press.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_72" href="#FNanchor_72" class="label">[72]</a> +Ap. J., 59, 197, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_73" href="#FNanchor_73" class="label">[73]</a> +Chapter VI, <a href="#Page_99">p. 99</a>.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_74" href="#FNanchor_74" class="label">[74]</a> +Chapter IX, <a href="#Page_137">p. 137</a>.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_75" href="#FNanchor_75" class="label">[75]</a> +Shapley, H. B. 805, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_76" href="#FNanchor_76" class="label">[76]</a> +Chapter XIII, p. <a href="#Page_188">p. 188</a>.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_77" href="#FNanchor_77" class="label">[77]</a> +Chapter V, <a href="#Page_56">p. 56</a>.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_78" href="#FNanchor_78" class="label">[78]</a> +Ap. J., 59, 197, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_79" href="#FNanchor_79" class="label">[79]</a> +Eddington, Zeit. f. Phys., 7, 371, 1921.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_80" href="#FNanchor_80" class="label">[80]</a> +Russell and Stewart (<i>loc. cit.</i>) show that there +are about 0.4 grams of matter above the photosphere per square +centimeter of surface.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_81" href="#FNanchor_81" class="label">[81]</a> +Phil. Mag., 26, 9, 1913.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_82" href="#FNanchor_82" class="label">[82]</a> +Phil. Mag., 37, 456, 1919.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_83" href="#FNanchor_83" class="label">[83]</a> +Zeit. f. Phys., 1, 1, 1920.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_84" href="#FNanchor_84" class="label">[84]</a> +Wright, Nature, 109, 810, 1920.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_85" href="#FNanchor_85" class="label">[85]</a> +Saha, Nature, 114, 155, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_86" href="#FNanchor_86" class="label">[86]</a> +Nicholson, M. N. R. A. S., 85, 253, 1925.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_87" href="#FNanchor_87" class="label">[87]</a> +Unpublished.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_88" href="#FNanchor_88" class="label">[88]</a> +Ap. J., 59, 197, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_89" href="#FNanchor_89" class="label">[89]</a> +M. N. R. A. S., 83, 403, 1923; 84, 499, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_90" href="#FNanchor_90" class="label">[90]</a> +H. C. 256, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_91" href="#FNanchor_91" class="label">[91]</a> +H. C. 258, 1924.</p> + +</div> +</div> + +<hr class="chap x-ebookmaker-drop"> + +<div class="chapter"> +<p><span class="pagenum" id="Page_46">[Pg 46]</span></p> + +<h2 class="nobreak" id="CHAPTER_IV">CHAPTER IV<br> +THE SOURCE AND COMPOSITION OF THE STELLAR +SPECTRUM</h2> +</div> + + +<p class="nind"> +THE spectrum of a laboratory source offers a somewhat inadequate +comparison with the spectrum of a star. Matter can be studied +terrestrially in small quantities only, and when a laboratory source +is used in obtaining a spectrum, all the contributing material is +collected into a very small region. With the stellar source it is quite +otherwise. An enormous mass of matter, spread over a very large region, +gives rise to the spectrum, and probably widely different physical +conditions prevail at the origin of light of different wave-lengths. +The present chapter contains a brief survey of the chief components +which go to make up the stellar spectrum.</p> + +<p>The spectrum of a star nearly always consists of a continuous +background, in which the energy distribution corresponds more or less +to that of a black body, and of absorption and emission lines and +bands. The observed stellar spectrum is the integrated contribution +from all parts of the disc, the unlined portion representing radiation +that passes undisturbed from the photosphere through the reversing +layer, and the light <i>within</i> any individual absorption line +coming from the greatest depth in the reversing layer that can be +penetrated by light of the corresponding frequency. This depth, which +is a function of the monochromatic coefficient of absorption for the +wave-length considered, is negligible when compared with the radius of +the star.</p> + + +<p class="nindc space-above2"> +DESCRIPTIVE DEFINITIONS</p> + + +<p>The solar atmosphere is probably qualitatively representative of all +normal stellar atmospheres. It has been satisfactorily described +<span class="pagenum" id="Page_47">[Pg 47]</span> +by Russell and Stewart:<a id="FNanchor_92" href="#Footnote_92" class="fnanchor">[92]</a> “At the top is a deep layer, the +chromosphere, in which the gases are held up by radiation pressure, +acting on individual atoms. The pressure and density in this layer +increase slowly downwards (as gravity somewhat overbalances radiation +pressure) and the pressure at its base may be of the order of +\(\displaystyle{10^{-7}\, \text{atmospheres}}\), or 0.0001 mm. of +mercury. Below this level, gravity is predominant in the equilibrium, +and the pressure increases rapidly with depth—the temperature +remaining nearly constant, and not far from 5000°, so long as the gases +are transparent. This region is the <i>reversing layer</i>. When the +pressure reaches 0.01 atmosphere, the general absorption by electron +collisions begins to render the gas hazy. This opacity increases +greatly with the pressure, and the reversing layer passes, by a fairly +rapid transition, into the <i>photosphere</i>, which on the scale on +which we have to study it resembles an opaque mass. As soon as the +opacity becomes important the temperature rises in accordance with +the theory of radiative equilibrium developed by Schwarzschild and +Eddington. The observed effective photospheric temperature is a mean +value for the layers from which radiation escapes to us.”</p> + +<p><span class="pagenum" id="Page_48">[Pg 48]</span></p> + +<p>The photosphere, as has been stated, is at an extremely small depth +compared with the radius of the star. Taking the sun as an example, +it is estimated by Russell and Stewart<a id="FNanchor_93" href="#Footnote_93" class="fnanchor">[93]</a> that the reversing layer, +which, with the chromosphere, is responsible for all the solar +phenomena that can be spectroscopically studied, consists of about four +tenths of a gram of matter per square centimeter of surface, and is +only a few hundred kilometers in thickness. As this embraces only about +\(10^{-11}\) of the mass and \(10^{-9}\) of the volume of the sun, it +is clear that the features that can be studied spectroscopically are +purely superficial, and that the larger aspects of stellar composition +and constitution are left essentially untouched.</p> + + +<p class="nindc space-above2"> +THE CONTINUOUS BACKGROUND</p> + + +<p>The continuous background of the spectrum represents the +photosphere—the deepest layers from which we receive light. The +energy that produces it is practically the total energy output of +the star. While the actual distribution of energy in the spectrum +probably conforms, in general, to that of a black body, the observed +distribution naturally deviates considerably. But when corrections have +been applied for atmospheric absorption, the resulting energy curves +so far obtained do not appear to furnish certain evidence of serious +deviation from blackness, although several investigators have suggested +that their measures lead to this conclusion.<a id="FNanchor_94" href="#Footnote_94" class="fnanchor">[94]</a><a id="FNanchor_95" href="#Footnote_95" class="fnanchor">[95]</a><a id="FNanchor_96" href="#Footnote_96" class="fnanchor">[96]</a></p> + +<p>If it is admitted that the energy distribution in the continuous +background is sensibly black, the application of the Planck and Wien +formulae furnishes methods of deriving the effective temperatures +of stars from the energy distribution and the position of maximum +intensity, respectively. The energy curve has therefore been +extensively studied, both photographically and photometrically, and our +present knowledge of stellar temperatures rests primarily upon work +of this nature. The solar spectrum has been the subject of exhaustive +photometric researches by Abbot<a id="FNanchor_97" href="#Footnote_97" class="fnanchor">[97]</a> and Wilsing,<a id="FNanchor_98" href="#Footnote_98" class="fnanchor">[98]</a> and the theory of +the energy distribution, and its relation to the law of darkening, have +been discussed by Lindblad,<a id="FNanchor_99" href="#Footnote_99" class="fnanchor">[99]</a> and by Milne.<a id="FNanchor_100" href="#Footnote_100" class="fnanchor">[100]</a> In a discussion of +the solar energy curve, Milne<a id="FNanchor_101" href="#Footnote_101" class="fnanchor">[101]</a> shows that the continuous spectrum +can be regarded as that of a black body displaced to the violet, and +that the displacement can be ascribed to the distortion of a normal +black body curve by the presence of strong absorption.</p> + +<p>H. H. Plaskett,<a id="FNanchor_102" href="#Footnote_102" class="fnanchor">[102]</a> in applying the wedge method of spectrophotometry +<span class="pagenum" id="Page_49">[Pg 49]</span> +to the same problem, took care to measure continuous background +intensities in spectral regions free from absorption lines stronger +than 0 per Angstrom, as measured on Rowland’s scale of intensities. +In this way he obtained a series of measures which should give a +distribution sensibly free from distortion. His result for the solar +temperature agrees more nearly with that derived from the solar +constant than do the results of previous observers, and therefore the +idea that the continuous background approximates to blackness is borne +out by observations made with the proper precautions. R. H. Fowler<a id="FNanchor_103" href="#Footnote_103" class="fnanchor">[103]</a> +has remarked that “there is no longer any large discrepancy between +the solar constant and the color temperatures, and one may hope that +further more accurate work will leave them in full agreement.”</p> + +<p><span class="pagenum" id="Page_50">[Pg 50]</span></p> + +<p>The position of maximum intensity governs the <i>color</i> of the +star, which is quite unrelated to the colors absorbed and radiated by +the atoms in the reversing layer. In some of the Wolf-Rayet stars, +apparently at very high temperatures and with atmospheres under special +conditions of excitation, the continuous spectrum appears extremely +faint, although there seems to be no reason for supposing that this is +not merely an effect of contrast with the powerful emission “bands.” +The writer believes that long exposures would demonstrate the presence +of continuous background for all such stars.<a id="FNanchor_104" href="#Footnote_104" class="fnanchor">[104]</a> In the spectra of +some gaseous nebulae, however, no continuous background has as yet +been observed,<a id="FNanchor_105" href="#Footnote_105" class="fnanchor">[105]</a> nor would any be expected, if our conception of +the tenuity of these bodies is correct, unless they shine partly by +pure reflection. (For example, the presence of some reflected starlight +is inferred from the existence of a continuous background for the +Orion nebula.) The transparency of gaseous nebulae to the light of +stars indicates that their general opacity is extremely low, and it +is this general opacity that is operative in producing the continuous +background of a photosphere.</p> + + +<p class="nindc space-above2"> +THE REVERSING LAYER</p> + + +<p>The reversing layer, comprising the layers above the photosphere, where +the general opacity has greatly decreased and selective opacity begins +to be appreciable, is responsible for the lines in the spectrum, which +form the major part of the material of stellar spectroscopy. When +the energy flowing out through the reversing layer in any specified +wave-length is less than the energy in the neighboring continuous +background, an absorption line is produced in the spectrum.</p> + +<p>Roughly speaking, if an atom absorbs the whole of the light of +any given frequency that reaches it from below, it will re-emit +all the energy so absorbed, and will in general do so in a random +direction.<a id="FNanchor_106" href="#Footnote_106" class="fnanchor">[106]</a> The intensity of the absorption line so formed +will then be about 50 per cent of the intensity in the neighboring +continuous background. This argument is merely illustrative; it must +suffice to point out that if pure selective absorption is operative the +spectrum will be crossed by lines that are considerably less intense +than the background. If, on the other hand, the energy leaving the +atmosphere with any wave-length is greater than the energy in the +neighboring continuous background, a bright line or “emission” line +appears in the spectrum. Actually, of course, it is no more an emission +line than is an ordinary Fraunhofer line, for the difference between +stellar absorption and emission is merely a matter of contrast with the +continuous background. Both kinds of line are “full of light.”</p> + + +<p class="nindc space-above2"> +ABSORPTION LINES</p> + + +<p>The absorption lines vary greatly among themselves and from star to +star, both in intensity and in general appearance. The metallic lines, +more particularly those of ionized atoms, are often extremely narrow +and sharp—a feature difficult to reproduce in the laboratory, and +referable to the very low pressures in the stellar atmosphere.<a id="FNanchor_107" href="#Footnote_107" class="fnanchor">[107]</a> +Other lines, such as those of the Balmer series of hydrogen, may be +<span class="pagenum" id="Page_51">[Pg 51]</span> +of considerable width, and spread out into wings that extend as much +as thirty Angstrom units on each side of the center of the line. Many +other lines are probably winged, but are not of sufficient strength for +the feature to be seen. The form of the wings and the general shape +of the line are of high significance, and should ultimately give much +information bearing on the structure of the stellar atmosphere.</p> + +<p>Although the absorption lines are commonly regarded as “dark,” the +foregoing section indicates that they should always have an appreciable +intensity even at their centers. Measures of the central intensities of +strong absorption lines have been published by various investigators, +and the results are not all in agreement. Schwarzschild<a id="FNanchor_108" href="#Footnote_108" class="fnanchor">[108]</a> gives +from a single measurement of the \(H\) and \(K\) lines in the solar spectrum +(center of disc) with the Hartmann microphotometer, wings ten Angstrom +units in width on either side of the line center, and a weakening of +the intensity of the light, from the continuous background to the +center of the line, of about two and a half magnitudes. Bottlinger’s +curves<a id="FNanchor_109" href="#Footnote_109" class="fnanchor">[109]</a> appear to lead to considerable intensities at the centers +of the hydrogen lines in the \(A\) stars. Others have suggested that the +central intensities are considerably lower. Abbot<a id="FNanchor_110" href="#Footnote_110" class="fnanchor">[110]</a> quotes estimates +ranging from one fifth to one tenth of the continuous background for +solar lines, and H. H. Plaskett<a id="FNanchor_111" href="#Footnote_111" class="fnanchor">[111]</a> states that the faintest stellar +lines have about one tenth the intensity of the continuous background, +as measured by his wedge method.<a id="FNanchor_112" href="#Footnote_112" class="fnanchor">[112]</a></p> + +<p>Determinations of central intensity by means of precise photometry +have been made by Kohlschütter<a id="FNanchor_113" href="#Footnote_113" class="fnanchor">[113]</a> and by Shapley,<a id="FNanchor_114" href="#Footnote_114" class="fnanchor">[114]</a> objective +prism spectra being used in both cases. Kohlschütter gives the results +of the analysis of the spectra of twenty-one stars of Classes \(A\) and +<span class="pagenum" id="Page_52">[Pg 52]</span> +\(F\) by means of the Hartmann microphotometer. The darkening from the +continuous background to the center of the line is tabulated in his +paper for \(H \delta\), \(H \epsilon +H\), \(K\), \(H \zeta\), and +\(H \eta\); it ranges for \(H \delta\) from 1.14 magnitudes for a Lyrae +to 0.42 magnitudes for \(\alpha\) Cygni. The corresponding central +intensities are 35 and 68 per cent of the intensity of the continuous +background. The method used by Shapley employed a special set of +apertures to obtain a graded series of images for a comparison of the +central intensity with that of the adjacent background. Although it +is not certain that all the very complex photographic and photometric +difficulties involved were overcome by this method, its results are +presumably entitled to greater weight than any other determinations +of central intensity hitherto made. The intensity in the hydrogen +absorption lines of Vega was ascertained to be about 25 per cent of +that of the background.</p> + + +<p class="nindc space-above2"> +SATURATION OF ABSORPTION LINES</p> + + +<p>The discussion outlined above presupposes that the substance producing +the absorption line in the reversing layer is present in quantities +great enough to absorb all the light of the appropriate wave-length, +subsequently re-emitting it and giving rise to an absorption line with +considerable central intensity. If the atom in question is present in +quantities too small for complete absorption to take place, the central +intensity of the line produced will of course be higher still. Such +atoms are designated “unsaturated.” Saturation has been described by +Russell<a id="FNanchor_115" href="#Footnote_115" class="fnanchor">[115]</a> as follows:—“For the strong lines ... the absorption in +the reversing layer is so great that a large increase in the number of +absorbing atoms present alters the strength of the line very little. +For the weak components ... absorption under ordinary conditions is +incomplete, and the strengthening (in the spectra of sunspots) is +noteworthy”—an increase in the amount of available material produces +an increase in the strength of the line. The strong components are +<span class="pagenum" id="Page_53">[Pg 53]</span> +saturated, the weak ones are not. It should be noted that here there is +an excess of atoms for the radiation. “Saturation” is used in another +sense when the word is applied to the conditions at the center of a +star,<a id="FNanchor_116" href="#Footnote_116" class="fnanchor">[116]</a> where there is an excess of radiation for the atoms present.</p> + + +<p class="nindc space-above2"> +EMISSION LINES</p> + + +<p>The emission lines observed in stellar spectra differ more widely among +themselves than do the absorption lines, and theory has so far been +less successful in suggesting the physical conditions under which they +may arise.<a id="FNanchor_117" href="#Footnote_117" class="fnanchor">[117]</a> The appearance of the bright-line flash spectrum of the +sun, from a region that gives no appreciable continuous spectrum, is +of interest in comparing emission and absorption lines. It is fairly +obvious that if the source of the flash spectrum had the photosphere +behind it, the bright line would appear as absorption lines—which is +indeed the case when the sun is ordinarily observed. Russell assigns +both the Fraunhofer lines and part of the flash spectrum to the same +region, namely the upper reversing layer. The high-level flash is, of +course, assigned to the lower chromosphere. The difference between +absorption and <i>narrow</i> emission is, as was pointed out in an +earlier paragraph, purely a matter of contrast. There has, however, +been no satisfactory explanation of how the phenomenon displayed by an +ordinary emission line can be produced—an atom that re-emits in some +wave-length more light than it receives in that wave-length. Some form +of “fluorescent” emission would seem to be involved, and the question +is evidently an important one for spectrum theory.</p> + +<p>The chief types of emission are found in (<i>a</i>) the long period +variables at maximum, (<i>b</i>) the emission \(B\) stars, (<i>c</i>) the \(O\) +stars, including the Wolf-Rayet stars. All these stars are apparently +very luminous.<a id="FNanchor_118" href="#Footnote_118" class="fnanchor">[118]</a> Emission is also found in some late dwarfs—for +example the \(H\) and \(K\) lines are reversed in the spectrum of +<span class="pagenum" id="Page_54">[Pg 54]</span> +<span class="allsmcap">61</span> Cygni,<a id="FNanchor_119" href="#Footnote_119" class="fnanchor">[119]</a> and doubly reversed in the solar spectrum. Furthermore the +spectra of gaseous nebulae are almost entirely composed of emission +lines; and completely abnormal types of stars, with spectra partly or +wholly composed of emission lines, might also be mentioned, notably +the novae,<a id="FNanchor_120" href="#Footnote_120" class="fnanchor">[120]</a> \(\eta\) Carinae,<a id="FNanchor_121" href="#Footnote_121" class="fnanchor">[121]</a> + Merrill’s “iron star,”<a id="FNanchor_122" href="#Footnote_122" class="fnanchor">[122]</a> Z +Andromedae,<a id="FNanchor_123" href="#Footnote_123" class="fnanchor">[123]</a> and<a id="FNanchor_124" href="#Footnote_124" class="fnanchor">[124]</a> B. D.+11°4673. The conditions under which +bright lines appear vary so widely that a single theory is manifestly +inadequate to account for the phenomenon in every case.</p> + + +<div class="footnotes"><h3>FOOTNOTES:</h3> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_92" href="#FNanchor_92" class="label">[92]</a> +Ap. J., 59, 197, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_93" href="#FNanchor_93" class="label">[93]</a> +<i>Ibid.</i></p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_94" href="#FNanchor_94" class="label">[94]</a> +H. H. Plaskett, Pub. Dom. Ap. Obs., 2, 258, 1923.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_95" href="#FNanchor_95" class="label">[95]</a> +C. G. Abbot, Ap. J., 60, 87, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_96" href="#FNanchor_96" class="label">[96]</a> +Baillaud, C. R., 178, 1604, 1923.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_97" href="#FNanchor_97" class="label">[97]</a> +The Sun, 1911.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_98" href="#FNanchor_98" class="label">[98]</a> +Potsdam Pub., 66, 1913.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_99" href="#FNanchor_99" class="label">[99]</a> +Lindblad, Upps. Univ. Arsskr., 1, 1920.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_100" href="#FNanchor_100" class="label">[100]</a> +Milne, Phil. Trans., 223A, 201, 1922.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_101" href="#FNanchor_101" class="label">[101]</a> +Milne, M. N. R. A. S., 81, 362 and 381, 1921.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_102" href="#FNanchor_102" class="label">[102]</a> +H. H. Plaskett, Pub. Dom. Ap. Obs., 2, 213, 1923.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_103" href="#FNanchor_103" class="label">[103]</a> +Observatory, 47, 160, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_104" href="#FNanchor_104" class="label">[104]</a> +H. C. 263, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_105" href="#FNanchor_105" class="label">[105]</a> +Hubble, Mt. W. Contr. 241, 1922.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_106" href="#FNanchor_106" class="label">[106]</a> +Milne, M. N. R. A. S., 84, 354, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_107" href="#FNanchor_107" class="label">[107]</a> +Chapter III, <a href="#Page_38">p. 38</a>.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_108" href="#FNanchor_108" class="label">[108]</a> +Sitz. d. Pr. Ak. d. Wiss., 47, 1183, 1914.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_109" href="#FNanchor_109" class="label">[109]</a> +A. N., 195, 117, 1913.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_110" href="#FNanchor_110" class="label">[110]</a> +The Sun, 251, 1911.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_111" href="#FNanchor_111" class="label">[111]</a> +Pub. Dom. Ap. Obs., 1, 325, 1922.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_112" href="#FNanchor_112" class="label">[112]</a> +Pub. Dom. Ap. Obs., 2, 213, 1923.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_113" href="#FNanchor_113" class="label">[113]</a> +A. N., 220, 326, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_114" href="#FNanchor_114" class="label">[114]</a> +H. B. 805, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_115" href="#FNanchor_115" class="label">[115]</a> +Am. Ast. Soc. Rep., 190, 1923.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_116" href="#FNanchor_116" class="label">[116]</a> +Eddington, Ap. J., 48, 205, 1918.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_117" href="#FNanchor_117" class="label">[117]</a> +M. C. Johnson, M. N. R. A. S., 85, 56, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_118" href="#FNanchor_118" class="label">[118]</a> +<i>Ibid.</i></p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_119" href="#FNanchor_119" class="label">[119]</a> +Adams and Joy, Pub. A. S. P., 36, 142, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_120" href="#FNanchor_120" class="label">[120]</a> +Chapter V, <a href="#Page_64">p. 64</a>.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_121" href="#FNanchor_121" class="label">[121]</a> +H. A., 28, 175, 1901.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_122" href="#FNanchor_122" class="label">[122]</a> +Pub. A. S. P. 36, 225, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_123" href="#FNanchor_123" class="label">[123]</a> +Br. A. Rep., 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_124" href="#FNanchor_124" class="label">[124]</a> +A. J. Cannon, H. B. 762, 1924.</p> + +</div> +</div> + +<hr class="chap x-ebookmaker-drop"> + +<div class="chapter"> +<p><span class="pagenum" id="Page_55">[Pg 55]</span></p> + +<h2 class="nobreak" id="CHAPTER_V">CHAPTER V<br> +ELEMENTS AND COMPOUNDS IN STELLAR ATMOSPHERES</h2> +</div> + +<p class="nind"> +THE identification of stellar lines and bands with those observed in +the laboratory has furnished a rich source of data for astrophysics. +About 25 per cent of the observed solar lines are assigned to elements +in Rowland’s Table of Solar Spectrum Wave-lengths. The majority of the +solar lines which are still unidentified are faint. Notwithstanding +practical difficulties of identification caused by blending, and the +consequent uncertainty of wave-length, most of the observed lines, at +least in the cooler stars, have been satisfactorily accounted for. +There remain some important strong lines and bands of unknown origin, +which have been usefully summarized by Baxandall.<a id="FNanchor_125" href="#Footnote_125" class="fnanchor">[125]</a></p> + +<p>The present chapter contains a summary of the stellar occurrence and +astrophysical behavior of the chief spectrum lines which are of known +origin and series relations. A few other lines, such as those of C++, +N++, and O+ are included, as their series relations will probably be +forthcoming in the near future. The observed chemical elements are +arranged in order of atomic number. At the conclusion of the chapter +the elements which have not been detected in stellar spectra are +enumerated. The series notation employed follows the system advocated +by Russell and Saunders,<a id="FNanchor_126" href="#Footnote_126" class="fnanchor">[126]</a> which appears to meet, more fully than +any other, the practical needs of modern spectroscopy.</p> + + +<p class="nindc space-above2"> +HYDROGEN (1)</p> + + +<p>Hydrogen is represented in stellar spectra by the Balmer series +(\(_2P-mD\)); the ultimate lines are those of the Lyman series +(\(_1S-mP\)) in the far ultra-violet, and cannot therefore be +<span class="pagenum" id="Page_56">[Pg 56]</span> +traced in the stellar spectrum. The occurrence of the secondary +spectrum of hydrogen, ascribed to the hydrogen molecule H₂, has been +suspected,<a id="FNanchor_127" href="#Footnote_127" class="fnanchor">[127]</a> but not definitely established. Only one of the lines +has been recorded, and this should almost certainly be attributed<a id="FNanchor_128" href="#Footnote_128" class="fnanchor">[128]</a> +to N++. The familiar Balmer series appear as emission lines in the +Wolf-Rayet stars, but normally they are absorption lines in all +succeeding classes.</p> + +<p>The intensity of the hydrogen lines is at a maximum<a id="FNanchor_129" href="#Footnote_129" class="fnanchor">[129]</a> in the +neighborhood of Class \(A_0\). They vary greatly in width, however, +within a given spectral class,<a id="FNanchor_130" href="#Footnote_130" class="fnanchor">[130]</a> and it is difficult to find a +method of photometry applicable to the comparison of lines of very +different widths. The maximum of the Balmer lines has been placed by +Menzel<a id="FNanchor_131" href="#Footnote_131" class="fnanchor">[131]</a> at \(A_3\). The writer is inclined to believe that no +significant maximum can in fact be derived for the Balmer lines; beyond +\(A_5\), however, their intensity falls off rapidly.</p> + +<p>It is peculiar to the Balmer series to appear in every class of the +normal stellar sequence, and its lines at maximum exceed in strength +the lines of every other element which appears in stellar spectra, +excepting those of ionized calcium.</p> + +<p>Although hydrogen is presumably unable to give rise to an “enhanced” +spectrum, as the atom only possesses one extra-nuclear electron, the +lines of the Balmer series share with those of neutral helium the +peculiarity of behaving like the lines of an ionized atom.<a id="FNanchor_132" href="#Footnote_132" class="fnanchor">[132]</a> They +are weakened in dwarf \(M\) stars, and greatly strengthened in the +cooler super-giants, such as \(\alpha\) Orionis. The peculiarity of +the astrophysical behavior of the hydrogen atom also appears in the +impossibly high value that is assigned by ionization theory to the +relative abundance of this element.<a id="FNanchor_133" href="#Footnote_133" class="fnanchor">[133]</a> An explanation, in terms +of metastability, has been suggested by Russell and Compton,<a id="FNanchor_134" href="#Footnote_134" class="fnanchor">[134]</a> +but although the hypothesis appears very satisfactory in the case +<span class="pagenum" id="Page_57">[Pg 57]</span> +of hydrogen, it is not applicable to the similar problem of helium. +Russell<a id="FNanchor_135" href="#Footnote_135" class="fnanchor">[135]</a> has remarked that “there seems to be a real tendency for +lines, for which both the ionization and excitation potentials are +large, to be much stronger than the elementary theory would indicate.”</p> + +<p>The hydrogen lines are often conspicuously winged. Measures of +the width and intensity-distribution of the wings are discussed +elsewhere.<a id="FNanchor_136" href="#Footnote_136" class="fnanchor">[136]</a> Wings are probably not peculiar to the hydrogen lines, +but the hydrogen wings can be studied because of their strength. The +feature is also seen in helium, calcium and iron lines, and wings of +greater or less strength are probably universal.</p> + +<p>The width of the hydrogen lines in \(A\) stars has been correlated with +absolute magnitude, and used for the estimation of luminosities.<a id="FNanchor_137" href="#Footnote_137" class="fnanchor">[137]</a> +It appears, however, that the line width may not furnish an accurate +measure of absolute magnitude, although it serves to discriminate stars +having the c-character from those of smaller luminosity.<a id="FNanchor_138" href="#Footnote_138" class="fnanchor">[138]</a> The +occurrence of wings seems, moreover, to be independent of line width +and of absolute magnitude.<a id="FNanchor_139" href="#Footnote_139" class="fnanchor">[139]</a> These questions are connected with +the problem of classifying the \(A\) stars, and are discussed in a later +chapter.<a id="FNanchor_140" href="#Footnote_140" class="fnanchor">[140]</a></p> + +<p>The continuous spectrum of hydrogen, beyond the limit of the Balmer +series, corresponding to the continuous radiation observed in the +laboratory for sodium by Wood,<a id="FNanchor_141" href="#Footnote_141" class="fnanchor">[141]</a> and for helium by Lyman,<a id="FNanchor_142" href="#Footnote_142" class="fnanchor">[142]</a> +was first noted in stellar spectra by Sir William Huggins.<a id="FNanchor_143" href="#Footnote_143" class="fnanchor">[143]</a> The +beginning of the band appears just to the red of the last Balmer +line observed.<a id="FNanchor_144" href="#Footnote_144" class="fnanchor">[144]</a> It appears, from work in progress at the Harvard +Observatory,<a id="FNanchor_145" href="#Footnote_145" class="fnanchor">[145]</a> that the limit is nearer to the violet, the higher +the luminosity, and in a nebular spectrum quoted by Hubble,<a id="FNanchor_146" href="#Footnote_146" class="fnanchor">[146]</a> it +almost coincides with the theoretical limit of the series.</p> + +<p><span class="pagenum" id="Page_58">[Pg 58]</span></p> + +<p>The largest number of hydrogen lines recorded is thirty-five, +measured by Mitchell<a id="FNanchor_147" href="#Footnote_147" class="fnanchor">[147]</a> in the flash spectrum. Thirty-three were +observed in emission by Evershed<a id="FNanchor_148" href="#Footnote_148" class="fnanchor">[148]</a> in the solar chromosphere, +and Deslandres<a id="FNanchor_149" href="#Footnote_149" class="fnanchor">[149]</a> traced twenty-nine in the spectrum of a bright +solar prominence. Twenty-seven Balmer lines have been observed by +Curtiss<a id="FNanchor_150" href="#Footnote_150" class="fnanchor">[150]</a> in the spectrum of \(\zeta\) Tauri—the greatest number +recorded for the spectrum of a star. The number of Balmer lines +observed is related in <a href="#CHAPTER_III">Chapter III</a> to the pressure in the reversing +layer.</p> + + +<p class="nindc space-above2"> +HELIUM (2)</p> + + +<p>Helium is represented in stellar spectra by the \(1{^{2}}S-m{^{2}}P\), +\(1{^{2}}P-m{^{2}}S\), \(1{^{2}}P-m{^{2}}D\), \(1S-mP, 1P-mD\), and possibly +the \(1P-mS\) series. Lines associated with these series appear almost +simultaneously as we progress through the \(O\) star sequence, attain +a maximum<a id="FNanchor_151" href="#Footnote_151" class="fnanchor">[151]</a> at \(B_3\), and have disappeared<a id="FNanchor_152" href="#Footnote_152" class="fnanchor">[152]</a> in normal \(A\) +stars. The ultimate lines are the \(_OS-mP\) series,<a id="FNanchor_153" href="#Footnote_153" class="fnanchor">[153]</a> in the far +ultra-violet, and cannot be traced in the stars.</p> + +<p>The helium lines vary much in width and definition and are often +winged. Their intensity does not certainly appear to vary with absolute +magnitude within a given spectral class, and they cannot therefore be +used in the estimation of spectroscopic parallaxes.<a id="FNanchor_154" href="#Footnote_154" class="fnanchor">[154]</a> The question +of absolute magnitude effects cannot be usefully pursued in the absence +of more reliable parallaxes, for the \(B\) stars, than are at present +available.</p> + +<p><span class="pagenum" id="Page_59">[Pg 59]</span></p> + +<p>Although the lines of helium do not appear in the normal \(A\) star, +they are observed in the spectrum of the super-giant \(\alpha\) Cygni, +where the pressure is presumably exceedingly low. The \(1{^{2}}P-m{^{2}}D\) +lines also appear in the flash spectrum.<a id="FNanchor_155" href="#Footnote_155" class="fnanchor">[155]</a></p> + + +<p class="nindc space-above2"> +IONIZED HELIUM</p> + + +<p>The lines of ionized helium appear only in the hottest stars, being +peculiar to the \(O\) sequence. The \(_4F-mG\) lines (the “Pickering,” +or “\(\zeta\) Puppis” series) are well marked in the hotter \(O\) stars, +although all the lines usually available are probably blended.<a id="FNanchor_156" href="#Footnote_156" class="fnanchor">[156]</a> +The alternate Pickering lines are practically superposed on the +Balmer lines, and the components were separated for several stars +of Class \(O\) by H. H. Plaskett.<a id="FNanchor_157" href="#Footnote_157" class="fnanchor">[157]</a> The “4686” series (\(_3D-mF\)) +appears in absorption in all the so-called “absorption \(O\) stars,” and +is even faintly seen in some \(B_0\) stars. The line at 4686 appears +very readily as an emission line, and the wide bright “band” at this +wave-length, which is a conspicuous feature of the Wolf-Rayet stars, of +gaseous nebulae, and of certain stages of a nova, is also presumably +due to ionized helium.</p> + + +<p class="nindc space-above2"> +LITHIUM (3)</p> + + +<p>The element lithium is represented in the sunspot spectrum by the +\(1{^{2}}S-m{^{2}}P\) (ultimate) doublet at 6707, which is not, however, +strong enough to be detected in stellar spectra. Russell<a id="FNanchor_158" href="#Footnote_158" class="fnanchor">[158]</a> has +called attention to the fact that this line is fainter, in the sun, +than would be anticipated from the terrestrial abundance of the +element. Compton<a id="FNanchor_159" href="#Footnote_159" class="fnanchor">[159]</a> has suggested that the faintness may be ascribed +to low atomic weight, and the consequent blurring of the line by a +Doppler effect, owing to the high velocity of thermal agitation.</p> + + +<p class="nindc space-above2"> +CARBON (6)</p> + + +<p>There is no evidence of the presence of neutral carbon in stellar +atmospheres. The apparent absence of the element is partly due to +the fact that the ultimate<a id="FNanchor_160" href="#Footnote_160" class="fnanchor">[160]</a> line is at 2478, too far in the +ultra-violet to be detected. The spectrum of neutral carbon is as yet +unclassified, and other lines cannot, therefore, be sought for in the +stellar spectrum. The temperature at which the element vaporizes is +<span class="pagenum" id="Page_60">[Pg 60]</span> +given by Kohn and Guckel<a id="FNanchor_161" href="#Footnote_161" class="fnanchor">[161]</a> as 4000°, and by Violle<a id="FNanchor_162" href="#Footnote_162" class="fnanchor">[162]</a> as 3800°. +The heat of vaporization has been evaluated by de Forcrand.<a id="FNanchor_163" href="#Footnote_163" class="fnanchor">[163]</a> At +stellar temperatures, the carbon present is probably vaporized, but +possibly it is largely in combination as cyanogen or as an oxide, since +spectra associated with these compounds appear in low-temperature stars.</p> + + +<p class="nindc space-above2"> +IONIZED CARBON</p> + + +<p>Ionized carbon<a id="FNanchor_164" href="#Footnote_164" class="fnanchor">[164]</a> is represented in the stellar spectrum by the +fundamental doublet (\(2{^{2}}D-m{^{2}}F\)), at 4267, and by the principal +doublet (\(3{^{2}}S-m{^{2}}P\)) at 6580. The occurrence of these lines +is of great interest. The line at 4267 is found in the \(O\) stars,<a id="FNanchor_165" href="#Footnote_165" class="fnanchor">[165]</a> +reaches a maximum at \(B_3\), and is last seen<a id="FNanchor_166" href="#Footnote_166" class="fnanchor">[166]</a> at \(B_9\). It also +occurs in the spectra of some gaseous nebulae.<a id="FNanchor_167" href="#Footnote_167" class="fnanchor">[167]</a> In the stellar +spectra in which it occurs, the line is sharp and clear, and, apart +from appearing as an emission line in certain stars of Class \(O\), it has +no abnormal stellar behavior.</p> + +<p>The principal doublet at 6580 has been said to occur in the Wolf-Rayet +spectrum,<a id="FNanchor_168" href="#Footnote_168" class="fnanchor">[168]</a><a id="FNanchor_169" href="#Footnote_169" class="fnanchor">[169]</a><a id="FNanchor_170" href="#Footnote_170" class="fnanchor">[170]</a> and to be much stronger than the fundamental +doublet. The identification has been discussed by Wright,<a id="FNanchor_171" href="#Footnote_171" class="fnanchor">[171]</a> and does +not appear to be very probable. A knowledge of the behavior of the line +at 6580 in the late \(O\) and early \(B\) stars is greatly to be desired.</p> + + +<p class="nindc space-above2"> +DOUBLY IONIZED CARBON</p> + + +<p>Merton<a id="FNanchor_172" href="#Footnote_172" class="fnanchor">[172]</a> has described a spectrum, produced under conditions +of high excitation, which shows several correspondences with the +emission bands of the Wolf-Rayet stars. His spectrum contains the +<span class="pagenum" id="Page_61">[Pg 61]</span> +fundamental and principal doublets of C+, as well as a number of other +lines, which have not as yet been assigned to series. Some of these +lines are probably to be referred<a id="FNanchor_173" href="#Footnote_173" class="fnanchor">[173]</a> to the atom of C++, and the +writer<a id="FNanchor_174" href="#Footnote_174" class="fnanchor">[174]</a> considers it unnecessary to assume the occurrence of a +higher degree of excitation for the Wolf-Rayet spectrum. Some of the +lines which are bright in the spectra of emission-line stars have +been attributed to C+++ on astrophysical grounds,<a id="FNanchor_175" href="#Footnote_175" class="fnanchor">[175]</a> and also from +a discussion of frequency differences.<a id="FNanchor_176" href="#Footnote_176" class="fnanchor">[176]</a> The four strongest groups +in Merton’s spectrum, however, consist of triplets, and this points +more probably to C++, as does also the ionization potential deduced +astrophysically<a id="FNanchor_177" href="#Footnote_177" class="fnanchor">[177]</a> from the behavior of the only group accessible in +ordinary stellar spectra. When the doublets due to C+, and the triplets +already mentioned, are accounted for in Merton’s spectrum, there +remain only two lines at 5696 and 5592. A line<a id="FNanchor_178" href="#Footnote_178" class="fnanchor">[178]</a> with the latter +wave-length is attributed by Fowler and Brooksbank<a id="FNanchor_179" href="#Footnote_179" class="fnanchor">[179]</a> to O++. The +evidence for stellar C+++ appears, therefore, to be inconclusive.</p> + + +<p class="nindc space-above2"> +COMPOUNDS OF CARBON</p> + + +<p><i>Cyanogen</i>. The bands headed at 3885, 4215, have been attributed +<a id="FNanchor_180" href="#Footnote_180" class="fnanchor">[180]</a> to the CN or the C₂N₂ radical, or to the molecule of nitrogen. +The assignment to a particular atom is essentially a question for +the terrestrial physicist, and to discuss it here would be out of +place.<a id="FNanchor_181" href="#Footnote_181" class="fnanchor">[181]</a> The bands are universally known as the “cyanogen bands,” +and this designation will therefore be adopted.</p> + +<p>The 3885 and 4215 bands are conspicuous in \(G\) and \(K\) stars of low +density,<a id="FNanchor_182" href="#Footnote_182" class="fnanchor">[182]</a> and furnish a valuable method for the measurement +<span class="pagenum" id="Page_62">[Pg 62]</span> +of absolute magnitude—a method which has been used both at Mount +Wilson<a id="FNanchor_183" href="#Footnote_183" class="fnanchor">[183]</a> and at Harvard.<a id="FNanchor_184" href="#Footnote_184" class="fnanchor">[184]</a> The band at 3885 is largely +responsible for cutting off the ultra-violet light of the cooler +stars.<a id="FNanchor_185" href="#Footnote_185" class="fnanchor">[185]</a></p> + +<p>Cyanogen absorption has been reported as early<a id="FNanchor_186" href="#Footnote_186" class="fnanchor">[186]</a> as \(A_0\), +and according to Lindblad<a id="FNanchor_187" href="#Footnote_187" class="fnanchor">[187]</a> it reaches a maximum at \(K_2\). +The cyanogen bands reach great intensity in the \(N\) stars, and are +indeed the most conspicuous feature of these spectra. Shane<a id="FNanchor_188" href="#Footnote_188" class="fnanchor">[188]</a> +places the maximum in Class \(N\), and is doubtless correct in so +doing. The maximum given by Lindblad refers to the series \(G\) +\(K\) \(M\), and the \(N\) stars are notoriously not members of that +sequence.<a id="FNanchor_189" href="#Footnote_189" class="fnanchor">[189]</a> Cyanogen is also a typical constituent of the comet-head +spectrum.<a id="FNanchor_190" href="#Footnote_190" class="fnanchor">[190]</a><a id="FNanchor_191" href="#Footnote_191" class="fnanchor">[191]</a><a id="FNanchor_192" href="#Footnote_192" class="fnanchor">[192]</a></p> + +<p><i>Carbon Oxides</i>. The band spectrum attributed to the CO +molecule,<a id="FNanchor_193" href="#Footnote_193" class="fnanchor">[193]</a><a id="FNanchor_194" href="#Footnote_194" class="fnanchor">[194]</a> +is a strong feature of the spectra of \(N\) and \(R\) +stars.<a id="FNanchor_195" href="#Footnote_195" class="fnanchor">[195]</a><a id="FNanchor_196" href="#Footnote_196" class="fnanchor">[196]</a> It is also the chief component of the spectrum of the +comet tail, which has been reproduced in the laboratory, at very low +pressures, by A. Fowler.<a id="FNanchor_197" href="#Footnote_197" class="fnanchor">[197]</a></p> + +<p><i>Swan Spectrum</i>. The bands of the Swan spectrum are clearly to +be assigned to some compound of carbon,<a id="FNanchor_198" href="#Footnote_198" class="fnanchor">[198]</a><a id="FNanchor_199" href="#Footnote_199" class="fnanchor">[199]</a> but the source is +not as yet certainly established. They are characteristic of the comet +head.<a id="FNanchor_200" href="#Footnote_200" class="fnanchor">[200]</a> Another band, presumably to be associated with the Swan +spectrum, was identified in the heads of nine comets by Baldet.<a id="FNanchor_201" href="#Footnote_201" class="fnanchor">[201]</a> +<span class="pagenum" id="Page_63">[Pg 63]</span> +The ordinary Swan bands are also identified in the comet tail.<a id="FNanchor_202" href="#Footnote_202" class="fnanchor">[202]</a></p> + +<p><i>Hydrocarbon</i>. The identity of the “\(G\)” band with the 4314 +hydrocarbon group was pointed out by Newall, Baxandall and Butler.<a id="FNanchor_203" href="#Footnote_203" class="fnanchor">[203]</a> +The strength of the band is increased, in the stellar spectrum, by the +superposition of the \(1^{3}P-m^{3}P'\) lines of calcium, and by the +\(1^{5}F-1^{5}D\) lines of titanium, as well as other metallic lines, +but the presence of the hydrocarbon band is certain, and is of the +highest interest. The “\(G\)” band is first seen in some spectra<a id="FNanchor_204" href="#Footnote_204" class="fnanchor">[204]</a> of +Class \(A\), and it attains a maximum at \(G\) or \(K\).</p> + +<p>The number of carbon compounds which occur lends plausibility to +the suggestion that much of the stellar carbon is in combination at +temperatures below 5000°.</p> + + +<p class="nindc space-above2"> +NITROGEN (7)</p> + + +<p>The spectrum of neutral nitrogen has not as yet been satisfactorily +analyzed into series.<a id="FNanchor_205" href="#Footnote_205" class="fnanchor">[205]</a> It is quite possible that the first +ionization that takes place is the ionization of the molecule,<a id="FNanchor_206" href="#Footnote_206" class="fnanchor">[206]</a> +which is accompanied by the production of the well known band spectrum. +This spectrum has not been observed in the stars; presumably it would +appear at lower temperatures than those involved in the coolest +spectral classes. It is, however, stated to be a conspicuous feature of +the spectrum of the aurora,<a id="FNanchor_207" href="#Footnote_207" class="fnanchor">[207]</a><a id="FNanchor_208" href="#Footnote_208" class="fnanchor">[208]</a> and it is found in the spectrum +of the comet head.<a id="FNanchor_209" href="#Footnote_209" class="fnanchor">[209]</a> These occurrences seem to point to very low +temperature and pressure at the source. It is possible that much of the +nitrogen present in cooler stars is in combination with carbon.<a id="FNanchor_210" href="#Footnote_210" class="fnanchor">[210]</a></p> + +<p>The green Aurora line was thought by Vegard<a id="FNanchor_211" href="#Footnote_211" class="fnanchor">[211]</a> to coincide +<span class="pagenum" id="Page_64">[Pg 64]</span> +with a line emitted in the laboratory by solid nitrogen. The conclusion was +questioned by McLennan and Shrum,<a id="FNanchor_212" href="#Footnote_212" class="fnanchor">[212]</a> who failed to produce the line +under similar conditions, and subsequently found a line, of the same +wave-length as the aurora line, in the spectrum of a mixture of oxygen +and helium.<a id="FNanchor_213" href="#Footnote_213" class="fnanchor">[213]</a> Various previous attempts to identify the aurora line +with a line produced in the laboratory had failed conspicuously.<a id="FNanchor_214" href="#Footnote_214" class="fnanchor">[214]</a></p> + + +<p class="nindc space-above2"> +IONIZED NITROGEN</p> + + +<p>The spectrum of ionized nitrogen has recently been analyzed by A. +Fowler.<a id="FNanchor_215" href="#Footnote_215" class="fnanchor">[215]</a> The line which is most conspicuous in stellar spectra is +the one at 3995 (\(P-S\)), which appears<a id="FNanchor_216" href="#Footnote_216" class="fnanchor">[216]</a> at \(B_0\) or earlier, +reaches maximum at \(B_5\), and is last seen at \(A_0\). Many of the +fainter lines<a id="FNanchor_217" href="#Footnote_217" class="fnanchor">[217]</a> are not observed.</p> + + +<p class="nindc space-above2"> +DOUBLY IONIZED NITROGEN</p> + + +<p>The lines of doubly ionized nitrogen were singled out by Lockyer<a id="FNanchor_218" href="#Footnote_218" class="fnanchor">[218]</a> +as showing “abnormal behavior”—they do not appear in the same +classes as the N+ line. The early work on the subject is discussed by +Baxandall.<a id="FNanchor_219" href="#Footnote_219" class="fnanchor">[219]</a> The most conspicuous lines are those at 4097, 4103, +and they attain great intensity in the \(O\) stars;<a id="FNanchor_220" href="#Footnote_220" class="fnanchor">[220]</a> they are, +for example, very conspicuous in <span class="allsmcap">29</span> Canis Majoris. H. H. +Plaskett<a id="FNanchor_221" href="#Footnote_221" class="fnanchor">[221]</a> places the maximum of the N++ lines in the Victoria class +\(O_7\). They are last seen in some \(B_0\) stars.</p> + +<p><span class="pagenum" id="Page_65">[Pg 65]</span></p> + +<p>The occurrence and behavior of the N+ and more especially the +N++ lines in the Nova spectrum has been the subject of numerous +investigations.<a id="FNanchor_222" href="#Footnote_222" class="fnanchor">[222]</a><a id="FNanchor_223" href="#Footnote_223" class="fnanchor">[223]</a><a id="FNanchor_224" href="#Footnote_224" class="fnanchor">[224]</a><a id="FNanchor_225" href="#Footnote_225" class="fnanchor">[225]</a><a id="FNanchor_226" href="#Footnote_226" class="fnanchor">[226]</a><a id="FNanchor_227" href="#Footnote_227" class="fnanchor">[227]</a></p> + + +<p class="nindc space-above2"> +OXYGEN (8)</p> + + +<p>The ultimate lines of neutral oxygen occur<a id="FNanchor_228" href="#Footnote_228" class="fnanchor">[228]</a> at a wave-length of +about 1300, and accordingly cannot be observed in the spectra of +stars. It was long supposed that neutral oxygen was entirely absent, +but the \(1^{5}S-m^{5}P\) triplet at 7700 is observed in the solar +spectrum,<a id="FNanchor_229" href="#Footnote_229" class="fnanchor">[229]</a> is strengthened in sunspots, and is strong in the high +level chromosphere.<a id="FNanchor_230" href="#Footnote_230" class="fnanchor">[230]</a> The ionization and excitation potentials +corresponding to the production of these lines are of the same order +as those for the Balmer series of hydrogen, and the astrophysical +behavior of the triplet should therefore be similar to that of the +hydrogen lines, with a maximum at or near \(A_0\). Special work in the +red is, however, required to trace the behavior of the series. The +second member, the triplet at 3947, is not certainly present in the +solar spectrum, and is not recorded for any star of Class \(A\). In the +laboratory, the second triplet is about as powerful as the first,<a id="FNanchor_231" href="#Footnote_231" class="fnanchor">[231]</a> +and its apparent weakness at the theoretical maximum is difficult to +explain.</p> + + +<p class="nindc space-above2"> +IONIZED OXYGEN</p> + + +<p>The spectrum of ionized oxygen should consist of pairs, and numerous +lines have been tabulated as belonging to this atom.<a id="FNanchor_232" href="#Footnote_232" class="fnanchor">[232]</a> The lines are +found in \(B\) stars, as seems first to have been noticed by Lunt.<a id="FNanchor_233" href="#Footnote_233" class="fnanchor">[233]</a> +According to the present writer,<a id="FNanchor_234" href="#Footnote_234" class="fnanchor">[234]</a> they are first seen at \(B_0\), +although H. H. Plaskett, working with slit spectra, records<a id="FNanchor_235" href="#Footnote_235" class="fnanchor">[235]</a> some +O+ lines in Class \(O\). The maximum of the O+ lines falls between \(B_1\) +and \(B_2\), and their disappearance is mentioned<a id="FNanchor_236" href="#Footnote_236" class="fnanchor">[236]</a> as a criterion +of Class \(B_3\).</p> + +<p><span class="pagenum" id="Page_66">[Pg 66]</span></p> + +<p>The lines at 4069, 4072, 4076, appear to form a triplet, but are more +probably two pairs with two of the lines coalesced. Some stronger lines +(<a href="#Page_207">page 207</a>) persist in Class \(B_5\).</p> + + +<p class="nindc space-above2"> +DOUBLY IONIZED OXYGEN</p> + + +<p>The spectrum of O++ has been tabulated by A. Fowler and +Brooksbank,<a id="FNanchor_237" href="#Footnote_237" class="fnanchor">[237]</a> but not analyzed into series. The lines of this +atom are certainly present<a id="FNanchor_238" href="#Footnote_238" class="fnanchor">[238]</a><a id="FNanchor_239" href="#Footnote_239" class="fnanchor">[239]</a> in the stars of Class \(O\). The +astrophysical behavior of the lines of doubly ionized oxygen has led to +the estimation of an ionization potential,<a id="FNanchor_240" href="#Footnote_240" class="fnanchor">[240]</a><a id="FNanchor_241" href="#Footnote_241" class="fnanchor">[241]</a> of 45 volts for +the corresponding atom.</p> + + +<p class="nindc space-above2"> +COMPOUNDS OF OXYGEN</p> + + +<p><i>Oxides.</i>—Numerous oxides, such as carbon monoxide CO, titanium +oxide TiO₂, zirconium oxide ZrO₂, and water H₂O, are present in the +cooler stars. The metallic oxides are discussed under the corresponding +metallic element. The occurrence of steam in the spectrum of the +sunspot was announced by Cortie,<a id="FNanchor_242" href="#Footnote_242" class="fnanchor">[242]</a> who supported his argument, +originally based upon the widening, over sunspots, of telluric water +vapor bands, by the observation that the presence of water vapor is +essential, in the laboratory, to the production of the spectrum of +magnesium hydride, which also occurs in the sunspot spectrum.<a id="FNanchor_243" href="#Footnote_243" class="fnanchor">[243]</a> It +is possible that the formation of oxides may account for the weakness +of the spectrum of neutral oxygen in the cooler stars, but this +explanation can hardly account for the absence of the second member of +the \(1^{5}S-m^{5}P\) series from the spectra of the \(A\) stars, where the +lines should have their maximum intensity.</p> + +<p><span class="pagenum" id="Page_67">[Pg 67]</span></p> + +<p><i>Ozone.</i>—The ozone bands which appear in solar and stellar +spectra have been shown by Fowler and Strutt<a id="FNanchor_244" href="#Footnote_244" class="fnanchor">[244]</a> to be of telluric +origin. The maximum thermal formation of ozone occurs <a id="FNanchor_245" href="#Footnote_245" class="fnanchor">[245]</a> at +\(\displaystyle{10^{-7}\, \text{atmospheres}}\) and 3500°, and thus its +presence in giant \(K\) and \(M\) stars might possibly be anticipated.</p> + + +<p class="nindc space-above2"> +SODIUM (11)</p> + + +<p>The ultimate lines (\(1^{2}S-m^{2}P\)) of the neutral atom of sodium +are the \(D\) lines, which lie at 5889, 5895. These are the only sodium +lines which are certainly identified in stellar spectra.<a id="FNanchor_246" href="#Footnote_246" class="fnanchor">[246]</a> They are +first seen in the later \(B\) classes, and appear to be strengthened in +cool stars, in accordance with theory.</p> + +<p>Stationary sodium lines are observed<a id="FNanchor_247" href="#Footnote_247" class="fnanchor">[247]</a> in \(\beta\) Scorpii, +\(\delta\) Orionis, and other Class \(B\) stars.<a id="FNanchor_248" href="#Footnote_248" class="fnanchor">[248]</a></p> + +<p>The \(D\) lines are said to show an absolute magnitude effect, being +strengthened in giant stars.<a id="FNanchor_249" href="#Footnote_249" class="fnanchor">[249]</a></p> + +<p>No lines of ionized sodium are found in stellar spectra, presumably +because they all lie in the far ultra-violet.</p> + + +<p class="nindc space-above2"> +MAGNESIUM (12)</p> + + +<p>The neutral atom of magnesium is represented in the solar spectrum by +the \(_1P-mD\), the \(1^{3}P-m^{3}D\), and the \(1^{3}P-m^{3}S\) series, +and the first triplet of the latter series constitutes the conspicuous +“b” group in the green. The “b” group and the second member of the +\(1^{3}P-m^{3}D\) series, the triplet near 3800, are first seen<a id="FNanchor_250" href="#Footnote_250" class="fnanchor">[250]</a> at +\(A_0\), have a maximum near \(K_2\) or \(K_5\), and are still strong +in the coolest stars examined. The \(_1S-m_{3}P\) series, represented +in the solar spectrum by a line at 4571, are faint ultimate lines; +the strong ultimate lines<a id="FNanchor_251" href="#Footnote_251" class="fnanchor">[251]</a> are the \(_1S-mP\) lines beginning at +2852, and are therefore outside the range of observed solar and stellar +spectra.</p> + + +<p class="nindc space-above2"> +IONIZED MAGNESIUM</p> + + +<p>The ionized magnesium atom gives rise to the important combination +doublet at 4481 (\(2^{2}D-m^{2}F\)). These lines appear in the \(O\) +sequence,<a id="FNanchor_252" href="#Footnote_252" class="fnanchor">[252]</a> reach maximum<a id="FNanchor_253" href="#Footnote_253" class="fnanchor">[253]</a> at \(A_2\) (not at \(A_0\), as stated +by several investigators), and are lost in the increasing strength of +<span class="pagenum" id="Page_68">[Pg 68]</span> +the iron line at the same wave-length, at about \(F_2\). The doublet +varies with absolute magnitude, and may be found to furnish a useful +criterion of that quantity. It has been used by H. H. Plaskett<a id="FNanchor_254" href="#Footnote_254" class="fnanchor">[254]</a> in +the estimation of the temperatures of some of the stars of Class \(O\).</p> + + +<p class="nindc space-above2"> +COMPOUNDS OF MAGNESIUM</p> + + +<p><i>Magnesium hydride.</i>—The compound magnesium hydride, MgH₂, which +has been studied in the laboratory by Brooks<a id="FNanchor_255" href="#Footnote_255" class="fnanchor">[255]</a> and Fowler,<a id="FNanchor_256" href="#Footnote_256" class="fnanchor">[256]</a> was +detected by the latter in the sunspot spectrum.<a id="FNanchor_257" href="#Footnote_257" class="fnanchor">[257]</a> It is perhaps +significant that the only other hydride reported in celestial spectra +is that of calcium, the next heavier alkaline earth after magnesium.</p> + + +<p class="nindc space-above2"> +ALUMINUM (13)</p> + + +<p>Neutral aluminum is represented in the solar spectrum by the +\(1^{2}P-m^{2}S\) lines, the series that constitutes the ultimate +lines in the third column elements of the periodic table.<a id="FNanchor_258" href="#Footnote_258" class="fnanchor">[258]</a> The +two conspicuous lines of the series in aluminum are those at 3944, +3957, and they are strengthened in cool stars,<a id="FNanchor_259" href="#Footnote_259" class="fnanchor">[259]</a> in accordance +with theory. They are especially mentioned as being strong in the +spectrum<a id="FNanchor_260" href="#Footnote_260" class="fnanchor">[260]</a> of <span class="allsmcap">61</span> Cygni, as might be expected for a dwarf +star. The \(1^{2}P-m^{2}D\) series is also traced in the solar +spectrum, but is too far in the ultra-violet to be studied effectively +in the stars.</p> + +<p>The series lines<a id="FNanchor_261" href="#Footnote_261" class="fnanchor">[261]</a> of Al+ and Al++, although they might be expected +in the \(B\) stars, apparently have not yet been traced in stellar +spectra.</p> + + +<p class="nindc space-above2"> +SILICON (14)</p> + + +<p>Four stages of the silicon atom are observed in stellar spectra. +The line at 3905 is found in the coolest stars, has an observed +<span class="pagenum" id="Page_69">[Pg 69]</span> +maximum<a id="FNanchor_262" href="#Footnote_262" class="fnanchor">[262]</a> at \(G_5\), and disappears at about \(F_0\). This line is +regarded by A. Fowler<a id="FNanchor_263" href="#Footnote_263" class="fnanchor">[263]</a> as the ultimate line of the neutral atom, +and on this basis an ionization potential of 10.6 volts was assigned to +silicon. In view of the fact that the line appears to have a maximum +within the stellar sequence, and is of temperature class II, according +to King,<a id="FNanchor_264" href="#Footnote_264" class="fnanchor">[264]</a> while the true ultimate line<a id="FNanchor_265" href="#Footnote_265" class="fnanchor">[265]</a> of silicon is at 2881, +it seems possible that 3905 is actually a subordinate line.</p> + + +<p class="nindc space-above2"> +IONIZED SILICON</p> + + +<p>Ionized silicon is represented by the lines 4128, 4131, which appear +at \(B_0\), attain maximum<a id="FNanchor_266" href="#Footnote_266" class="fnanchor">[266]</a> at \(A_0\), and disappear at \(F_0\). +These lines are of especial interest, as they form the characteristic +feature of the “silicon stars” which occur in the early \(A\) classes. +The silicon stars are specially discussed<a id="FNanchor_267" href="#Footnote_267" class="fnanchor">[267]</a> +in <a href="#CHAPTER_XII">Chapter XII</a>.</p> + + +<p class="nindc space-above2"> +DOUBLY IONIZED SILICON</p> + + +<p>The lines associated with the atom Si++ which appear in stellar spectra +are the three at the wave-lengths 4552, 4568, 4574. These lines +are first seen at \(B_0\), have a maximum<a id="FNanchor_268" href="#Footnote_268" class="fnanchor">[268]</a> between \(B_1\) and +\(B_2\), and disappear at \(B_3\). Fowler<a id="FNanchor_269" href="#Footnote_269" class="fnanchor">[269]</a> regards these lines as +constituting a principal triplet; it might be expected, however, that +principal lines would show a more persistent maximum.</p> + + +<p class="nindc space-above2"> +TRIPLY IONIZED SILICON</p> + + +<p><span class="pagenum" id="Page_70">[Pg 70]</span></p> + +<p>The atom of silicon which has lost three electrons is the most highly +ionized atom of which we have certain evidence in stellar spectra. The +lines at 4089, 4096, and 4116 are strong<a id="FNanchor_270" href="#Footnote_270" class="fnanchor">[270]</a> among the cooler \(O\) +stars, and are last seen at Class \(B_0\). The hotter \(O\) stars, such +as H.D. 165052, do not display the lines of Si+++, and probably the +intensity of the lines has fallen, owing to the temperature, which is +above that required for the maximum of these lines.</p> + + +<p class="nindc space-above2"> +SULPHUR (16)</p> + + +<p>The spectrum of neutral sulphur which has hitherto been analyzed is +chiefly in the far ultra-violet,<a id="FNanchor_271" href="#Footnote_271" class="fnanchor">[271]</a> and is therefore not traceable in +the sun or stars.</p> + +<p>Two sets of sulphur lines, differing in astrophysical behavior, were +noted by Lockyer<a id="FNanchor_272" href="#Footnote_272" class="fnanchor">[272]</a> at 4163, 4174, 4815, and at 4253, 4285, 4295. +These lines have been attributed by the writer,<a id="FNanchor_273" href="#Footnote_273" class="fnanchor">[273]</a> and by Fowler and +Milne,<a id="FNanchor_274" href="#Footnote_274" class="fnanchor">[274]</a> to S+ and S++ respectively. The S+ lines appear to be in +pairs, and the S++ lines suggest a triplet, although one of the three +lines is extremely faint in stellar spectra, and it would be expected +that the once and twice ionized spectra of sulphur would display even +and odd multiplicities respectively. The two series have maxima at +\(B_8\) and at \(B_1\), but the stellar intensities of the lines are +small. An amplification of our knowledge of stellar sulphur is greatly +to be desired.</p> + + +<p class="nindc space-above2"> +POTASSIUM (19)</p> + + +<p>The ultimate lines<a id="FNanchor_275" href="#Footnote_275" class="fnanchor">[275]</a> of potassium (\(1^{2}S-m^{2}P\)) are at 7664 +and 7699, and have been traced in the solar spectrum, although they +are very faint. They appear to be absent from the flash spectrum.<a id="FNanchor_276" href="#Footnote_276" class="fnanchor">[276]</a> +Russell<a id="FNanchor_277" href="#Footnote_277" class="fnanchor">[277]</a> expresses the opinion that they persist, with rising +temperature, as far as \(F_8\) in the stellar sequence.</p> + + +<p class="nindc space-above2"> +CALCIUM (20)</p> + + +<p>The element calcium is extensively represented in stellar spectra. +The ultimate line of the neutral atom is at 4227 (\(_1S-mP\)) and +appears at \(A_0\). The line increases in strength in all cooler +stars, in accordance with theory, and has a distinct variation with +<span class="pagenum" id="Page_71">[Pg 71]</span> +absolute magnitude. The \(^{3}P-^{3}P'\), \(^{3}P-^{3}D\) and \(^{3}D-^{3}F\) +multiplets<a id="FNanchor_278" href="#Footnote_278" class="fnanchor">[278]</a> are satisfactorily identified in the solar spectrum +and can be traced with certainty in the spectra of stars cooler than +\(F_0\). The \(_1P-mS\), \(_1P-mD\), \(_1D-mF\), and \(_1D-mP\) lines +appear to be present with the appropriate intensities in the sun, but +are too faint to be seen with small dispersion. Thus all the classified +lines of calcium which are strong in laboratory spectra have been +traced in the spectra of the sun and stars.</p> + + +<p class="nindc space-above2"> +IONIZED CALCIUM</p> + + +<p>The \(H\) and \(K\) lines of ionized calcium are seen throughout the +stellar sequence, and reach a maximum within the \(K\) type,<a id="FNanchor_279" href="#Footnote_279" class="fnanchor">[279]</a> where +their intensity is greater than that attained by any other line in any +class. They vary with absolute magnitude.<a id="FNanchor_280" href="#Footnote_280" class="fnanchor">[280]</a> In the sun the lines +are doubly reversed, and they are probably singly reversed<a id="FNanchor_281" href="#Footnote_281" class="fnanchor">[281]</a> in +<span class="allsmcap">61</span> Cygni.</p> + +<p>Stationary calcium lines have long been known to occur in the +spectra of certain spectroscopic binaries, having first been noticed +by Hartmann<a id="FNanchor_282" href="#Footnote_282" class="fnanchor">[282]</a> for \(\delta\) Orionis. Various “calcium cloud” +hypotheses have been advanced to account for the phenomenon. It +appears, from several considerations, notably the apparent small +oscillation of the calcium lines with the same period as the star, that +there is some physical connection between the two. Lee<a id="FNanchor_283" href="#Footnote_283" class="fnanchor">[283]</a> discussed +the idea that the system of <span class="allsmcap">9</span> Camelopardalis was surrounded +by a cloud of calcium vapor, which, as he showed, could be made to +account for the behavior of the lines of ionized calcium. The same idea +was discussed by J. S. Plaskett, who suggested that we might “assume +that the absorbing material is near to or envelopes the stars, which is +probable from its wide distribution, and in this form it combines the +two original hypotheses of interstellar and surrounding clouds.”<a id="FNanchor_284" href="#Footnote_284" class="fnanchor">[284]</a> +The \(D\) lines of sodium<a id="FNanchor_285" href="#Footnote_285" class="fnanchor">[285]</a> +<span class="pagenum" id="Page_72">[Pg 72]</span> +and possibly the hydrogen lines<a id="FNanchor_286" href="#Footnote_286" class="fnanchor">[286]</a> +have been added to the list of stationary lines, and Plaskett<a id="FNanchor_287" href="#Footnote_287" class="fnanchor">[287]</a> has +suggested that the ultimate lines of the ionized atoms of strontium and +barium should also show the effect, which has not yet, however, been +observed.</p> + + +<p class="nindc space-above2"> +SCANDIUM (21)</p> + + +<p>The element scandium<a id="FNanchor_288" href="#Footnote_288" class="fnanchor">[288]</a> is represented in the solar spectrum +by faint lines corresponding to the multiplets \(1^{2}D-5^{2}D'\), +\(1^{2}D-4{^{2}}D'\), \(1^{2}D-2F'\). The multiplet \(1^{4}F-1^{4}F'\) +may possibly be present, but the lines are very weak. The element is +not recorded in the spectra of stars; most of the lines are unsuitably +placed in the green.</p> + + +<p class="nindc space-above2"> +IONIZED SCANDIUM</p> + + +<p>Six multiplets of ionized scandium, out of the eight tabulated by +Meggers, Kiess, and Walters<a id="FNanchor_289" href="#Footnote_289" class="fnanchor">[289]</a> appear in the solar spectrum, and +all the corresponding lines have been traced in Rowland’s tables. The +intensity of two of the lines is great enough for their behavior to be +traced through the stellar sequence, and they are greatly enhanced in +the spectra of the c-stars. The ultimate lines are near 3600, but in +the solar spectrum they are less powerful than the lines near 3500.</p> + +<p><a href="#TABLE_XI">Table XI</a> on page 73 contains, in successive columns, the series +relations, the wave-length as determined in the laboratory, the +intensity, the temperature class, and the attribution, solar intensity, +and wave-length given by Rowland, for the six multiplets which lie +within the observed range of the solar spectrum. Ultimate lines are +designated by an asterisk.</p> + + +<p class="nindc space-above2"> +TITANIUM (22)</p> + + +<p><span class="pagenum" id="Page_73">[Pg 73]</span></p> + +<p>The spectrum of titanium is so rich in lines, and is so largely +represented in stellar spectra, that a tabulation would occupy an undue +amount of space.</p> + +<h2><a id="TABLE_XI">TABLE XI</a></h2> + +<table class="autotable"> +<thead><tr> +<th class="tdc bb bt2 br">Series</th> +<th class="tdc bb bt2 br">Wave-Lenght</th> +<th class="tdc bb bt2 br"> Int. </th> +<th class="tdc bb bt2 br"> Cl. </th> +<th class="tdc bb bt2 br">Attribution</th> +<th class="tdc bb bt2 br"> Int. </th> +<th class="tdc bb bt2">Wave-Lenght</th> +</tr> +</thead> +<tbody><tr> +<td class="tdc br">\(^*3D_3-^3F_4\)</td> +<td class="tdc br">3613.84</td> +<td class="tdc br">60</td> +<td class="tdc br">II</td> +<td class="tdc br">-, Sc</td> +<td class="tdc br">4</td> +<td class="tdc">3613.947</td> +</tr><tr> +<td class="tdc br">\(^3D_3-^3F_3\)</td> +<td class="tdc br">3645.31</td> +<td class="tdc br">30</td> +<td class="tdc br">III</td> +<td class="tdc br">Sc?, -</td> +<td class="tdc br">3</td> +<td class="tdc">3645.475</td> +</tr><tr> +<td class="tdc br">\(^*3D_2-^3F_3\)</td> +<td class="tdc br">3630.76</td> +<td class="tdc br">50</td> +<td class="tdc br">II</td> +<td class="tdc br"> </td> +<td class="tdc br">4</td> +<td class="tdc">3630.876</td> +</tr><tr> +<td class="tdc br">\(^3D_3-^3F_2\)</td> +<td class="tdc br">3666.54</td> +<td class="tdc br">3</td> +<td class="tdc br">III</td> +<td class="tdc br"></td> +<td class="tdc br">1</td> +<td class="tdc">3666.676</td> +</tr><tr> +<td class="tdc br">\(^3D_2-^3F_2\)</td> +<td class="tdc br">3651.81</td> +<td class="tdc br">25</td> +<td class="tdc br">III</td> +<td class="tdc br">-, Sc</td> +<td class="tdc br">4</td> +<td class="tdc">3651.940</td> +</tr><tr> +<td class="tdc br">\(^*3D_1-^3F_2\)</td> +<td class="tdc br">3642.79</td> +<td class="tdc br">40</td> +<td class="tdc br">II</td> +<td class="tdc br">Sc</td> +<td class="tdc br">2</td> +<td class="tdc">3642.912</td> +</tr><tr> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc"></td> +</tr><tr> +<td class="tdc br">\(^3D_3-^3D'_3\)</td> +<td class="tdc br">3572.53</td> +<td class="tdc br">50</td> +<td class="tdc br">II</td> +<td class="tdc br">-, Sc</td> +<td class="tdc br">6</td> +<td class="tdc">3572.71</td> +</tr><tr> +<td class="tdc br">\(^3D_2-^3D'_3\)</td> +<td class="tdc br">3558.55</td> +<td class="tdc br">20</td> +<td class="tdc br">II</td> +<td class="tdc br">(Fe</td> +<td class="tdc br">8</td> +<td class="tdc">3558.672)</td> +</tr><tr> +<td class="tdc br">\(^3D_3-^3D'_2\)</td> +<td class="tdc br">3590.48</td> +<td class="tdc br">20</td> +<td class="tdc br">II</td> +<td class="tdc br"></td> +<td class="tdc br">2</td> +<td class="tdc">3590.609</td> +</tr><tr> +<td class="tdc br">\(^3D_2-^3D'_2\)</td> +<td class="tdc br">3576.35</td> +<td class="tdc br">35</td> +<td class="tdc br">II</td> +<td class="tdc br">-, Sc?</td> +<td class="tdc br">3</td> +<td class="tdc">3576.527</td> +</tr><tr> +<td class="tdc br">\(^3D_1-^3D'_2\)</td> +<td class="tdc br">3567.70</td> +<td class="tdc br">20</td> +<td class="tdc br">II</td> +<td class="tdc br"></td> +<td class="tdc br">4</td> +<td class="tdc">3567.835</td> +</tr><tr> +<td class="tdc br">\(^3D_2-^3D'_1\)</td> +<td class="tdc br">3589.64</td> +<td class="tdc br">20</td> +<td class="tdc br">II</td> +<td class="tdc br"></td> +<td class="tdc br">5</td> +<td class="tdc">3589.773</td> +</tr><tr> +<td class="tdc br">\(^3D_1-^3D'_1\)</td> +<td class="tdc br">3580.94</td> +<td class="tdc br">30</td> +<td class="tdc br">II</td> +<td class="tdc br"></td> +<td class="tdc br">5</td> +<td class="tdc">3581.067</td> +</tr><tr> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc"></td> +</tr><tr> +<td class="tdc br">\(^3P_2-^3P'_2\)</td> +<td class="tdc br">5657.89</td> +<td class="tdc br">25</td> +<td class="tdc br">V E</td> +<td class="tdc br">Y, -</td> +<td class="tdc br">2</td> +<td class="tdc">5658.09</td> +</tr><tr> +<td class="tdc br">\(^3P_2-^3P'_1\)</td> +<td class="tdc br">5684.21</td> +<td class="tdc br">12</td> +<td class="tdc br">V E</td> +<td class="tdc br"></td> +<td class="tdc br">1</td> +<td class="tdc">5684.415</td> +</tr><tr> +<td class="tdc br">\(^3P_1-^3P'_2\)</td> +<td class="tdc br">5640.99</td> +<td class="tdc br">15</td> +<td class="tdc br">V E</td> +<td class="tdc br"></td> +<td class="tdc br">2</td> +<td class="tdc">5641.206</td> +</tr><tr> +<td class="tdc br">\(^3P_1-^3P'_1\)</td> +<td class="tdc br">5667.16</td> +<td class="tdc br">9</td> +<td class="tdc br">V E</td> +<td class="tdc br"></td> +<td class="tdc br">0</td> +<td class="tdc">5667.368</td> +</tr><tr> +<td class="tdc br">\(^3P_0-^3P'_1\)</td> +<td class="tdc br">5658.35</td> +<td class="tdc br">8</td> +<td class="tdc br">V E</td> +<td class="tdc br"></td> +<td class="tdc br">0</td> +<td class="tdc">5658.561</td> +</tr><tr> +<td class="tdc br">\(^3P_1-^3P'_0\)</td> +<td class="tdc br">5669.05</td> +<td class="tdc br">10</td> +<td class="tdc br">V E</td> +<td class="tdc br"></td> +<td class="tdc br">1</td> +<td class="tdc">5669.258</td> +</tr><tr> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc"></td> +</tr><tr> +<td class="tdc br">\(^3F_4-^3F'_4\)</td> +<td class="tdc br">4374.46</td> +<td class="tdc br">40</td> +<td class="tdc br">III E</td> +<td class="tdc br">Sc, Fe?</td> +<td class="tdc br">3</td> +<td class="tdc">3374.628</td> +</tr><tr> +<td class="tdc br">\(^3F_4-^3F'_3\)</td> +<td class="tdc br">4420.66</td> +<td class="tdc br">2</td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"><span class="tight">00</span></td> +<td class="tdc">4420.832</td> +</tr><tr> +<td class="tdc br">\(^3F_3-^3F'_4\)</td> +<td class="tdc br">4354.60</td> +<td class="tdc br">5</td> +<td class="tdc br">V E</td> +<td class="tdc br"></td> +<td class="tdc br">1</td> +<td class="tdc">4354.776</td> +</tr><tr> +<td class="tdc br">\(^3F_3-^3F'_3\)</td> +<td class="tdc br">4400.38</td> +<td class="tdc br">30</td> +<td class="tdc br">III E</td> +<td class="tdc br">Sc</td> +<td class="tdc br">3</td> +<td class="tdc">4400.555</td> +</tr><tr> +<td class="tdc br">\(^3F_2-^3F'_2\)</td> +<td class="tdc br">4431.35</td> +<td class="tdc br">3</td> +<td class="tdc br">V E</td> +<td class="tdc br"></td> +<td class="tdc br">0</td> +<td class="tdc">4431.525</td> +</tr><tr> +<td class="tdc br">\(^3F_2-^3F'_3\)</td> +<td class="tdc br">4384.80</td> +<td class="tdc br">6</td> +<td class="tdc br">IV E</td> +<td class="tdc br"></td> +<td class="tdc br">0</td> +<td class="tdc">4384.986</td> +</tr><tr> +<td class="tdc br">\(^3F_2-^3F'_2\)</td> +<td class="tdc br">4415.55</td> +<td class="tdc br">20</td> +<td class="tdc br">III E</td> +<td class="tdc br"></td> +<td class="tdc br">2</td> +<td class="tdc">4415.722</td> +</tr><tr> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc"></td> +</tr><tr> +<td class="tdc br">\(^3F_4-^3D'_3\)</td> +<td class="tdc br">4314.09</td> +<td class="tdc br">60</td> +<td class="tdc br">III E</td> +<td class="tdc br">Sc</td> +<td class="tdc br">3</td> +<td class="tdc">4314.248</td> +</tr><tr> +<td class="tdc br">\(^3F_3-^3D'_3\)</td> +<td class="tdc br">4294.77</td> +<td class="tdc br">8</td> +<td class="tdc br">IV E</td> +<td class="tdc br">Zr</td> +<td class="tdc br">2</td> +<td class="tdc">4294.932</td> +</tr><tr> +<td class="tdc br">\(^3F_3-^3D'_2\)</td> +<td class="tdc br">4320.73</td> +<td class="tdc br">50</td> +<td class="tdc br">III E</td> +<td class="tdc br">Sc</td> +<td class="tdc br">3</td> +<td class="tdc">4320.90</td> +</tr><tr> +<td class="tdc br">\(^3F_2-^3D'_3\)</td> +<td class="tdc br">4279.95</td> +<td class="tdc br">1</td> +<td class="tdc br">-</td> +<td class="tdc br"></td> +<td class="tdc br">-</td> +<td class="tdc">----</td> +</tr><tr> +<td class="tdc br">\(^3F_2-^3D'_2\)</td> +<td class="tdc br">4305.70</td> +<td class="tdc br">10</td> +<td class="tdc br">IV E</td> +<td class="tdc br"></td> +<td class="tdc br">2</td> +<td class="tdc">4305.871</td> +</tr><tr> +<td class="tdc bb br">\(^3F_2-^3D'_1\)</td> +<td class="tdc bb br">4325.00</td> +<td class="tdc bb br">40</td> +<td class="tdc bb br">III E</td> +<td class="tdc bb br">Sc</td> +<td class="tdc bb br">4</td> +<td class="tdc bb">4325.152</td> +</tr> +</tbody> +</table> + + +<p>From an examination of Rowland’s tables of the solar spectrum, it +appears that the fainter components of the multiplets invariably +accompany the stronger ones, thus making the identifications certain. +<span class="pagenum" id="Page_74">[Pg 74]</span> +Only the stronger components are, however, powerful enough to appear in +stellar spectra, with the dispersions ordinarily used.</p> + +<p>The following multiplets, as analyzed by Russell<a id="FNanchor_290" href="#Footnote_290" class="fnanchor">[290]</a> and Kiess,<a id="FNanchor_291" href="#Footnote_291" class="fnanchor">[291]</a> +are definitely present: \(1^{3}F-1^{3}F'\), \(1^{3}F-2^{3}F'\), +\(1^{3}F-1^{3}G'\), \(2^{3}F-6^{3}G'\), \(1^{3}F-1^{3}D'\), +\(1^{3}F-2^{3}D'\), \(1^{3}P-2^{3}P'\), \(1^{5}F-2^{5}G'\), +\(1^{5}F-2^{5}F'\), \(1^{5}F-2^{5}D'\), \(1^{5}P-1^{5}P'\). Doubtfully +present are: \(1^{5}P-4^{5}D'\), \(2^{3}F-5^{3}F'\).</p> + +<p>The maximum of these lines is difficult to determine; they are not +well placed for measurement, many of the most important are seriously +blended, and all are rather faint, even at maximum. They are first +seen<a id="FNanchor_292" href="#Footnote_292" class="fnanchor">[292]</a> at Class \(A_2\), and their maximum appears to be<a id="FNanchor_293" href="#Footnote_293" class="fnanchor">[293]</a> at +\(K_2\) or \(K_5\).</p> + +<p>The solar intensities of the lines of both neutral and ionized titanium +fall off regularly with increasing excitation potential. The subject is +discussed in <a href="#CHAPTER_VII">Chapter VII</a>, as part of the evidence for the validity of +the Saha theory.<a id="FNanchor_294" href="#Footnote_294" class="fnanchor">[294]</a></p> + + +<p class="nindc space-above2"> +IONIZED TITANIUM</p> + + +<p>The lines of ionized titanium are about as strong in the solar spectrum +as those of the neutral atom. Many of them appear, with the lines of +the ionized iron atom, with abnormal strength in the spectra of the +c-stars.<a id="FNanchor_295" href="#Footnote_295" class="fnanchor">[295]</a> The following multiplets<a id="FNanchor_296" href="#Footnote_296" class="fnanchor">[296]</a> are present in the solar +spectrum: \(1^{4}F-1^{4}G'\), \(1^{4}F-1^{4}F'\), \(1^{4}F-1^{4}P'\), +\(2^{4}F-1^{4}G'\), \(2^{4}F-1^{4}F'\), \(2^{4}F-1^{4}P'\), +\(1^{2}F-1^{2}G'\), \(1^{2}F-1^{2}F'\), \(1^{2}F-1^{2}D'\), +\(1^{2}D-1^{2}F'\), \(1^{2}D-1^{2}D'\), \(1^{2}G-1^{2}F'\), +\(1^{2}G-1^{2}G'\), \(1^{4}P-1^{2}D\), \(1^{4}P-1^{4}D'\), +\(1^{2}P-1^{2}D'\), \(1^{2}P-1^{4}D'\), \(1^{2}H-1^{2}G'\), +\(1^{2}H-2^{2}G'\), \(2^{2}G-2^{2}G'\), \(2^{2}G-2^{2}F'\), +\(2^{2}G-2^{2}G'\). Doubtfully present are \(1^{2}P-1^{2}F'\), +\(2^{2}D-1^{2}F'\), \(2^{2}D-1^{2}D'\), \(2^{2}F-2^{2}G'\). The lines +which are especially enhanced in the c-stars are: \(2^{2}G-2^{2}F'\), +\(1^{4}P-1^{2}D'\), \(1^{2}D-1^{2}F'\), \(1^{2}G-1^{2}D'\), +\(1^{2}G-1^{2}F'\), \(1^{2}P-1^{2}2D'\), \(1^{2}H-1^{2}G'\), +\(2^{2}P-1^{2}S'\).</p> + +<p>The lines of ionized titanium come to a maximum at about Class \(F_5\), +but a significant maximum is difficult to determine, for the lines are +<span class="pagenum" id="Page_75">[Pg 75]</span> +extremely sensitive to absolute magnitude. Menzel,<a id="FNanchor_297" href="#Footnote_297" class="fnanchor">[297]</a> using \(\beta\) +Cassiopeiae (classed by him as \(F_0\)) for his typical star, found a +maximum development of lines in that star. The present writer,<a id="FNanchor_298" href="#Footnote_298" class="fnanchor">[298]</a> +using the wider selection of stars enumerated in the appendix, +obtains \(G_0\) as the maximum for Ti+. A glance at the measures<a id="FNanchor_299" href="#Footnote_299" class="fnanchor">[299]</a> +will indicate that the position of the maximum is in any case very +uncertain, as the intensity does not change smoothly in going from +class to class.</p> + + +<p class="nindc space-above2"> +COMPOUNDS OF TITANIUM</p> + + +<p>The absorption bands of titanium oxide, TiO₂, are the characteristic +flutings<a id="FNanchor_300" href="#Footnote_300" class="fnanchor">[300]</a><a id="FNanchor_301" href="#Footnote_301" class="fnanchor">[301]</a> +of the stars of Class \(M\), and the strength of these +bands has been proposed<a id="FNanchor_302" href="#Footnote_302" class="fnanchor">[302]</a> as a criterion of class for the stars +in which they are found. It is perhaps noteworthy that titanium, +zirconium, and carbon, the only elements which give oxides in stellar +spectra (hydrogen excepted) belong to the fourth group of the periodic +system.</p> + + +<p class="nindc space-above2"> +VANADIUM (23)</p> + + +<p>The vanadium lines are best identified by intensity from Rowland’s +table. The following multiplets<a id="FNanchor_303" href="#Footnote_303" class="fnanchor">[303]</a> are present in the solar +spectrum: \(1^{6}D-2^{6}D'\), \(1^{6}D-2^{6}F'\), \(1^{6}D-1^{6}P'\), +\(1^{4}D-3^{4}F'\), \(1^{4}F-1^{4}F'\), \(1^{4}F-1^{4}G'\), +\(1^{4}F-1^{4}G'\). The \(1^{6}D-2^{6}D'\) multiplet is well seen in +stellar spectra from \(F_0\) onwards, and increases in strength as +cooler stars are approached.<a id="FNanchor_304" href="#Footnote_304" class="fnanchor">[304]</a> Slipher<a id="FNanchor_305" href="#Footnote_305" class="fnanchor">[305]</a> called attention to +the strength in \(\omicron\) Ceti of the vanadium group near 4400, +presumably the two multiplets \(1^{6}D-1^{6}P'\), \(1^{6}D-2^{6}F'\), +with excitation potential 0.28 volts.</p> + +<p><span class="pagenum" id="Page_76">[Pg 76]</span></p> + + +<p class="nindc space-above2"> +IONIZED VANADIUM</p> + +<p>Three multiplets, all far in the ultra-violet, are tabulated for +ionized vanadium by Meggers, Kiess, and Walters,<a id="FNanchor_306" href="#Footnote_306" class="fnanchor">[306]</a> and two of them +are within the range of Rowland’s table. All the lines of these, the +\(^{3}F-^{3}F\) and \(^{5}F-^{5}G\) multiplets, have been satisfactorily +identified with solar lines. The strength of the ultimate lines of +ionized vanadium, which occur in the multiplet last named, is a little +greater, in the solar spectrum, than that of the strongest lines of the +neutral atom, at 4379, which are also ultimate lines.</p> + +<p>The following tabulation contains, in the same form as <a href="#TABLE_XI">Table XI</a>, the +data respecting the two multiplets which are identified in the solar +spectrum.</p> + +<h2><a id="TABLE_XII">TABLE XII</a></h2> + +<table class="autotable"> +<thead><tr> +<th class="tdc bb bt2 br">Series</th> +<th class="tdc bb bt2 br">Wave-Lenght</th> +<th class="tdc bb bt2 br"> Int. </th> +<th class="tdc bb bt2 br"> Cl. </th> +<th class="tdc bb bt2 br">Attribution</th> +<th class="tdc bb bt2 br"> Int. </th> +<th class="tdc bb bt2">Wave-Lenght</th> +</tr> +</thead> +<tbody><tr> +<td class="tdc br">\(^3F_4-^3F'_4\)</td> +<td class="tdc br">3727.348</td> +<td class="tdc br">20</td> +<td class="tdc br">-</td> +<td class="tdc br"></td> +<td class="tdc br">1</td> +<td class="tdc">3727.488</td> +</tr><tr> +<td class="tdc br">\(^3F_3-^3F'_4\)</td> +<td class="tdc br">3760.230</td> +<td class="tdc br">5</td> +<td class="tdc br">-</td> +<td class="tdc br"></td> +<td class="tdc br">1</td> +<td class="tdc">3760.364</td> +</tr><tr> +<td class="tdc br">\(^3F_4-^3F'_3\)</td> +<td class="tdc br">3718.163</td> +<td class="tdc br">3</td> +<td class="tdc br">-</td> +<td class="tdc br"></td> +<td class="tdc br">\(_0N\)</td> +<td class="tdc">3718.291</td> +</tr><tr> +<td class="tdc br">\(^3F_3-^3F'_3\)</td> +<td class="tdc br">3750.873</td> +<td class="tdc br">15</td> +<td class="tdc br">-</td> +<td class="tdc br"></td> +<td class="tdc br">2</td> +<td class="tdc">3751.015</td> +</tr><tr> +<td class="tdc br">\(^3F_2-^3F'_3\)</td> +<td class="tdc br">3778.359</td> +<td class="tdc br">3</td> +<td class="tdc br">-</td> +<td class="tdc br">(Fe</td> +<td class="tdc br">3</td> +<td class="tdc">3778.463)</td> +</tr><tr> +<td class="tdc br">\(^3F_3-^3F'_2\)</td> +<td class="tdc br">3743.63</td> +<td class="tdc br">3</td> +<td class="tdc br">-</td> +<td class="tdc br">(Cr</td> +<td class="tdc br">1</td> +<td class="tdc">37243.726)</td> +</tr><tr> +<td class="tdc br">\(^3F_2-^3F'_2\)</td> +<td class="tdc br">3770.976</td> +<td class="tdc br">10</td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br">2</td> +<td class="tdc">3771.116</td> +</tr><tr> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc"></td> +</tr><tr> +<td class="tdc br">*\(^5F_5-^5G'_6\)</td> +<td class="tdc br">3093.10</td> +<td class="tdc br">40</td> +<td class="tdc br">III Er</td> +<td class="tdc br"></td> +<td class="tdc br">\(_2N\)</td> +<td class="tdc">3093.229</td> +</tr><tr> +<td class="tdc br">\(^5F_5-^5G'_5\)</td> +<td class="tdc br">3121.144</td> +<td class="tdc br">20</td> +<td class="tdc br">IV E</td> +<td class="tdc br">V</td> +<td class="tdc br">4</td> +<td class="tdc">3121.270</td> +</tr><tr> +<td class="tdc br">*\(^5F_4-^5G'_5\)</td> +<td class="tdc br">3102.301</td> +<td class="tdc br">40</td> +<td class="tdc br">III Er</td> +<td class="tdc br">V</td> +<td class="tdc br">3</td> +<td class="tdc">3102.404</td> +</tr><tr> +<td class="tdc br">\(^5F_5-^5G'_4\)</td> +<td class="tdc br">3145.35</td> +<td class="tdc br">-</td> +<td class="tdc br">-</td> +<td class="tdc br"></td> +<td class="tdc br">3</td> +<td class="tdc">3145.484</td> +</tr><tr> +<td class="tdc br">\(^5F_4-^5G'_4\)</td> +<td class="tdc br">3126.221</td> +<td class="tdc br">25</td> +<td class="tdc br">IV E</td> +<td class="tdc br">V, Fe</td> +<td class="tdc br">5</td> +<td class="tdc">3126.319</td> +</tr><tr> +<td class="tdc br">*\(^5F_3-^5G'_4\)</td> +<td class="tdc br">3110.710</td> +<td class="tdc br">30</td> +<td class="tdc br">III Er</td> +<td class="tdc br">Ti, V</td> +<td class="tdc br">\(_5Nd\)?</td> +<td class="tdc">3110.810</td> +</tr><tr> +<td class="tdc br">\(^5F_4-^5G'_3\)</td> +<td class="tdc br">3145.979</td> +<td class="tdc br">5</td> +<td class="tdc br">V Er</td> +<td class="tdc br">Zr</td> +<td class="tdc br">1</td> +<td class="tdc">3146.091</td> +</tr><tr> +<td class="tdc br">\(^5F_3-^5G'_3\)</td> +<td class="tdc br">3130.270</td> +<td class="tdc br">25</td> +<td class="tdc br">III E</td> +<td class="tdc br">V</td> +<td class="tdc br">3</td> +<td class="tdc">3130.380</td> +</tr><tr> +<td class="tdc br">*\(^5F_2-^5G'_3\)</td> +<td class="tdc br">3118.382</td> +<td class="tdc br">30</td> +<td class="tdc br">III Er</td> +<td class="tdc br">V</td> +<td class="tdc br">3</td> +<td class="tdc">3118.498</td> +</tr><tr> +<td class="tdc br">\(^5F_3-^5G'_2\)</td> +<td class="tdc br">3145.344</td> +<td class="tdc br">10</td> +<td class="tdc br">IV E</td> +<td class="tdc br"></td> +<td class="tdc br">3</td> +<td class="tdc">3145.484</td> +</tr><tr> +<td class="tdc br">\(^5F_2-^5G'_2\)</td> +<td class="tdc br">3133.336</td> +<td class="tdc br">20</td> +<td class="tdc br">III E</td> +<td class="tdc br">V</td> +<td class="tdc br">2</td> +<td class="tdc">3133.449</td> +</tr><tr> +<td class="tdc bb br">*\(^5F_1-^5G'_2\)</td> +<td class="tdc bb br">3125.286</td> +<td class="tdc bb br">40</td> +<td class="tdc bb br">III Er</td> +<td class="tdc bb br"></td> +<td class="tdc bb br">5</td> +<td class="tdc bb">3125.399</td> +</tr> +</tbody> +</table> + + +<p><span class="pagenum" id="Page_77">[Pg 77]</span></p> + + +<p class="nindc space-above2"> +CHROMIUM (24)</p> + + +<p>The lines of chromium were classified by Catalan,<a id="FNanchor_307" href="#Footnote_307" class="fnanchor">[307]</a> and those which +occur in the sun are comprised in the following multiplets:<a id="FNanchor_308" href="#Footnote_308" class="fnanchor">[308]</a> +\(1^{7}S-1^{7}P\), \(1^{7}S-1^{5}P\), \(1^{7}S-2^{7}P\), +\(1^{5}S-1^{7}P\), \(1^{5}S-1^{5}P'\), \(1^{5}S-1^{5}P\), +\(1^{5}D-1^{5}P\), \(1^{5}D-1^{5}P'\), \(1^{5}D-1^{5}P\), +\(1^{7}P-2^{7}S\), \(1^{7}P-1^{7}D\), \(1^{7}P-2^{7}D\).</p> + +<p>The ultimate lines \(1^{7}S-1^{7}P\), at 4254, 4274, 4289 increase +with advancing type.<a id="FNanchor_309" href="#Footnote_309" class="fnanchor">[309]</a> The maximum for subordinate lines<a id="FNanchor_310" href="#Footnote_310" class="fnanchor">[310]</a> is at +\(M_1\).</p> + + +<p class="nindc space-above2"> +IONIZED CHROMIUM</p> + + +<p>Of the six multiplets of ionized chromium tabulated by Meggers, Kiess, +and Walters,<a id="FNanchor_311" href="#Footnote_311" class="fnanchor">[311]</a> only two are within the measured range of the solar +spectrum, but every line in these two multiplets accords satisfactorily +in wave-length and intensity with a line in Rowland’s table. The +ultimate lines are in the neighborhood of 2800, and are therefore +unattainable. The lines, and the solar intensities, are contained in +the appended table.</p> + +<h2><a id="TABLE_XIII">TABLE XIII</a></h2> + +<table class="autotable"> +<thead><tr> +<th class="tdc bb bt2 br">Series</th> +<th class="tdc bb bt2 br">Wave-Lenght</th> +<th class="tdc bb bt2 br"> Int. </th> +<th class="tdc bb bt2 br">Attribution</th> +<th class="tdc bb bt2 br"> Int. </th> +<th class="tdc bb bt2">Wave-Lenght</th> +</tr> +</thead> +<tbody><tr> +<td class="tdc br">\(^4D_1-^4P_2\)</td> +<td class="tdc br">3328.34</td> +<td class="tdc br">3</td> +<td class="tdc br"></td> +<td class="tdc br">1</td> +<td class="tdc">3328.487</td> +</tr><tr> +<td class="tdc br">\(^4D_1-^4P_1\)</td> +<td class="tdc br">3336.33</td> +<td class="tdc br">5</td> +<td class="tdc br">Cr</td> +<td class="tdc br">2</td> +<td class="tdc">3336.477</td> +</tr><tr> +<td class="tdc br">\(^4D_2-^4P_3\)</td> +<td class="tdc br">3324.06</td> +<td class="tdc br">3</td> +<td class="tdc br"></td> +<td class="tdc br">\(_4N\)</td> +<td class="tdc">3324.19</td> +</tr><tr> +<td class="tdc br">\(^4D_2-^4P_2\)</td> +<td class="tdc br">3339.80</td> +<td class="tdc br">10</td> +<td class="tdc br">Co, Cr</td> +<td class="tdc br">3</td> +<td class="tdc">3339.932</td> +</tr><tr> +<td class="tdc br">\(^4D_2-^4P_1\)</td> +<td class="tdc br">3347.83</td> +<td class="tdc br">6</td> +<td class="tdc br">Cr</td> +<td class="tdc br">3</td> +<td class="tdc">3347.970</td> +</tr><tr> +<td class="tdc br">\(^4D_3-^4P_3\)</td> +<td class="tdc br">3342.58</td> +<td class="tdc br">10</td> +<td class="tdc br">Cr</td> +<td class="tdc br">3</td> +<td class="tdc">3342.717</td> +</tr><tr> +<td class="tdc br">\(^4D_3-^4P_2\)</td> +<td class="tdc br">3358.50</td> +<td class="tdc br">10</td> +<td class="tdc br">Ti, Cr</td> +<td class="tdc br">4</td> +<td class="tdc">3358.649</td> +</tr><tr> +<td class="tdc br">\(^4D_4-^4P_3\)</td> +<td class="tdc br">3368.04</td> +<td class="tdc br">20</td> +<td class="tdc br">Cr, -</td> +<td class="tdc br">\(_5d\)?</td> +<td class="tdc">3368.193</td> +</tr><tr> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc"></td> +</tr><tr> +<td class="tdc br">\(^4D_4-^4F_5\)</td> +<td class="tdc br">3132.04</td> +<td class="tdc br">20</td> +<td class="tdc br">-, Cr</td> +<td class="tdc br">4</td> +<td class="tdc">3132.169</td> +</tr><tr> +<td class="tdc br">\(^4D_3-^4F_4\)</td> +<td class="tdc br">3124.97</td> +<td class="tdc br">20</td> +<td class="tdc br">Cr</td> +<td class="tdc br">4</td> +<td class="tdc">3125.109</td> +</tr><tr> +<td class="tdc br">\(^4D_4-^4F_4\)</td> +<td class="tdc br">3147.22</td> +<td class="tdc br">5</td> +<td class="tdc br">Cr</td> +<td class="tdc br">3</td> +<td class="tdc">3147.350</td> +</tr><tr> +<td class="tdc br">\(^4D_2-^4F_3\)</td> +<td class="tdc br">3120.36</td> +<td class="tdc br">15</td> +<td class="tdc br">Cr, -</td> +<td class="tdc br">3</td> +<td class="tdc">3120.481</td> +</tr><tr> +<td class="tdc br">\(^4D_3-^4F_3\)</td> +<td class="tdc br">3136.69</td> +<td class="tdc br">5</td> +<td class="tdc br">Cr, Co</td> +<td class="tdc br">3</td> +<td class="tdc">3136.822</td> +</tr><tr> +<td class="tdc br">\(^4D_4-^4F_3\)</td> +<td class="tdc br">3159.10</td> +<td class="tdc br">1</td> +<td class="tdc br"></td> +<td class="tdc br">0</td> +<td class="tdc">3159.225</td> +</tr><tr> +<td class="tdc br">\(^4D_1-^4F_2\)</td> +<td class="tdc br">3118.65</td> +<td class="tdc br">10</td> +<td class="tdc br">Cr, -</td> +<td class="tdc br">2</td> +<td class="tdc">3118.764</td> +</tr><tr> +<td class="tdc br">\(^4D_2-^4F_2\)</td> +<td class="tdc br">3128.68</td> +<td class="tdc br">5</td> +<td class="tdc br">Cr, -</td> +<td class="tdc br">2</td> +<td class="tdc">3128.819</td> +</tr><tr> +<td class="tdc bb br">\(^4D_2-^4F_2\)</td> +<td class="tdc bb br">3145.07</td> +<td class="tdc bb br">2</td> +<td class="tdc bb br"></td> +<td class="tdc bb br">2</td> +<td class="tdc bb">3145.251</td> +</tr> +</tbody> +</table> + + +<p><span class="pagenum" id="Page_78">[Pg 78]</span></p> + + +<p class="nindc space-above2"> +MANGANESE (25)</p> + + +<p>The lines of manganese are conspicuous in stellar spectra, and all +the classified lines<a id="FNanchor_312" href="#Footnote_312" class="fnanchor">[312]</a> within the range of Rowland’s table are +found in the solar spectrum, namely the multiplets \(1^{6}S-1^{6}P\), +\(1^{6}S-2^{6}P\), \(1^{6}D-2^{6}P\), \(1^{6}D-^{6}D'\), +\(1^{8}P-2^{8}D\), \(1^{8}P-1^{8}S\), \(1^{4}D-1^{4}P\), +\(1^{6}P-3^{6}D\), \(1^{6}D-1^{6}F\), \(1^{4}D-1^{4}F'\). The ultimate +lines \(1^{6}S-1^{6}P\) are at 4030, and constitute a conspicuous group +in the solar spectrum. They are well seen in the cooler stars, and are +progressively strengthened with advancing type.<a id="FNanchor_313" href="#Footnote_313" class="fnanchor">[313]</a> They first appear +at \(A_0\). The \(1^{6}D-1^{6}D'\) multiplet, at 4018, 4041, 4055, +4084, etc., has a maximum, according to Menzel,<a id="FNanchor_314" href="#Footnote_314" class="fnanchor">[314]</a> at \(K_5\).</p> + + +<p class="nindc space-above2"> +IONIZED MANGANESE</p> + + +<p>Meggers, Kiess, and Walters<a id="FNanchor_315" href="#Footnote_315" class="fnanchor">[315]</a> give one multiplet of ionized +manganese, and this is within the range of Rowland’s table. The +multiplet was previously picked out by Catalan<a id="FNanchor_316" href="#Footnote_316" class="fnanchor">[316]</a> as being analogous +to the arc multiplet \(1^{6}D-2^{6}P\). All the lines can be +satisfactorily identified with lines in the solar spectrum, as in the +following table.</p> + +<h2><a id="TABLE_XIV">TABLE XIV</a></h2> + +<table class="autotable"> +<thead><tr> +<th class="tdc bb bt2 br">Series</th> +<th class="tdc bb bt2 br">Wave-Lenght</th> +<th class="tdc bb bt2 br"> Int. </th> +<th class="tdc bb bt2 br"> Cl. </th> +<th class="tdc bb bt2 br">Attribution</th> +<th class="tdc bb bt2 br"> Int. </th> +<th class="tdc bb bt2">Wave-Lenght</th> +</tr> +</thead> +<tbody><tr> +<td class="tdc br">\(^5P_3-^5D_4\)</td> +<td class="tdc br">3441.999</td> +<td class="tdc br">9</td> +<td class="tdc br">V</td> +<td class="tdc br">Mn</td> +<td class="tdc br">6</td> +<td class="tdc">3442.118</td> +</tr><tr> +<td class="tdc br">\(^5P_3-^5D_3\)</td> +<td class="tdc br">3474.050</td> +<td class="tdc br">7</td> +<td class="tdc br">V</td> +<td class="tdc br">Mn</td> +<td class="tdc br">2</td> +<td class="tdc">3474.197</td> +</tr><tr> +<td class="tdc br">\(^5P_2-^5D_3\)</td> +<td class="tdc br">3460.332</td> +<td class="tdc br">8</td> +<td class="tdc br">V</td> +<td class="tdc br">Mn, -</td> +<td class="tdc br">\(_4d\)?</td> +<td class="tdc">3460.460</td> +</tr><tr> +<td class="tdc br">\(^5P_2-^5D_2\)</td> +<td class="tdc br">3496.815</td> +<td class="tdc br">4</td> +<td class="tdc br">V</td> +<td class="tdc br">Co, Mn</td> +<td class="tdc br">3</td> +<td class="tdc">3496.952</td> +</tr><tr> +<td class="tdc br">\(^5P_2-^5D_3\)</td> +<td class="tdc br">3482.918</td> +<td class="tdc br">7</td> +<td class="tdc br">V</td> +<td class="tdc br">Mn, -</td> +<td class="tdc br">\(_5d\)</td> +<td class="tdc">3483.047</td> +</tr><tr> +<td class="tdc br">\(^5P_1-^5D_2\)</td> +<td class="tdc br">3474.13</td> +<td class="tdc br">6</td> +<td class="tdc br">V</td> +<td class="tdc br">Mn</td> +<td class="tdc br">2</td> +<td class="tdc">3474.287</td> +</tr><tr> +<td class="tdc br">\(^5P_2-^5D_2\)</td> +<td class="tdc br">3497.540</td> +<td class="tdc br">6</td> +<td class="tdc br">V</td> +<td class="tdc br">Mn</td> +<td class="tdc br">3</td> +<td class="tdc">3497.668</td> +</tr><tr> +<td class="tdc br">\(^5P_2-^5D_1\)</td> +<td class="tdc br">3488.618</td> +<td class="tdc br">8</td> +<td class="tdc br">V</td> +<td class="tdc br">Mn</td> +<td class="tdc br">4</td> +<td class="tdc">3488.817</td> +</tr><tr> +<td class="tdc bb br">\(^5P_1-^5D_0\)</td> +<td class="tdc bb br">3495.810</td> +<td class="tdc bb br">8</td> +<td class="tdc bb br">V</td> +<td class="tdc bb br">Mn</td> +<td class="tdc bb br">2</td> +<td class="tdc bb">3495.974</td> +</tr> +</tbody> +</table> + + +<p><span class="pagenum" id="Page_79">[Pg 79]</span></p> + + +<p class="nindc space-above2"> +IRON (26)</p> + + +<p>The extensive occurrence of the arc lines of iron in the stellar +spectrum is well known. The following multiplets<a id="FNanchor_317" href="#Footnote_317" class="fnanchor">[317]</a> have been +traced in the solar spectrum, and the corresponding lines are also +to be traced in the spectra of the cooler stars: \(1^{5}D-1^{7}D'\), +\(1^{5}D-1^{5}D'\), \(1^{5}F-1^{5}D'\), \(1^{5}F-1^{3}F'\), +\(1^{5}F-1^{5}F'\), \(1^{5}F-2^{5}D'\), \(1^{3}F-1^{3}F'\), +\(1^{3}F-2^{5}D'\), \(1^{3}F-2^{5}F'\), \(1^{3}F-1^{5}G\), +\(1^{3}F-1^{3}G'\), \(1^{3}F-2^{3}F'\), \(1^{5}P-3^{5}D\), +\(1^{5}D-m^{5}F\), \(1^{5}F-m^{5}F\), \(1^{7}F-m^{7}D\). The iron lines +have, in general,<a id="FNanchor_318" href="#Footnote_318" class="fnanchor">[318]</a> a maximum at \(K_2\), but the only ultimate +lines which are well shown in stellar spectra, the \(1^{6}D-1^{7}F\) +lines near 4480, increase with advancing type to the end of the +sequence.<a id="FNanchor_319" href="#Footnote_319" class="fnanchor">[319]</a></p> + +<p>The following lines are used as criteria of absolute magnitude by +Harper and Young:<a id="FNanchor_320" href="#Footnote_320" class="fnanchor">[320]</a> 4202, 4250, 4272 (\(1^{3}F-1^{3}G\)), 4072 +(\(1^{3}F-2^{3}F'\)), 4482 (\(1^{5}D-1^{7}F\)).</p> + + +<p class="nindc space-above2"> +IONIZED IRON</p> + + +<p><span class="pagenum" id="Page_80">[Pg 80]</span></p> + +<p>The lines of ionized iron are strong in F stars of high luminosity, and +are especially conspicuous in the stars which have the c-character. +Menzel<a id="FNanchor_321" href="#Footnote_321" class="fnanchor">[321]</a> places the maximum at \(A_7\), and the writer<a id="FNanchor_322" href="#Footnote_322" class="fnanchor">[322]</a> finds it +at \(F_5\). The following multiplets, as classified by Russell,<a id="FNanchor_323" href="#Footnote_323" class="fnanchor">[323]</a> +occur in the solar spectrum: \(1^{4}G-1^{4}F'\), \(1^{4}G-1^{4}D'\), +\(2^{4}F-1^{4}F'\), \(2^{4}F-1^{4}D'\), \(2^{4}F-1^{4}P'\), +\(2^{4}P-1^{4}F'\), \(2^{4}P-1^{4}D'\), \(2^{4}P-1^{4}P'\), +\(1^{4}P-1^{4}F'\), \(1^{4}P-1^{4}P'\), \(1^{4}D-1^{4}F'\), +\(1^{4}D-1^{4}D'\), \(1^{4}D-1^{4}P'\), \(1^{4}F-1^{4}F'\), +\(1^{4}F-1^{4}D'\), \(1^{4}F-1^{4}P'\), \(1S-1^{4}F'\), +\(1S-1^{4}D'\), \(1S-1^{4}P'\), \(1^{4}F-1^{4}G\), \(1^{4}F-1^{4}D\). +Doubtfully present are: \(1^{6}D-1^{4}F'\), \(1^{6}D-1^{4}P'\), +\(1^{6}D-1^{4}D'\). The ionized iron lines are strengthened, as are +other enhanced lines, over sunspots, and many of the fainter components +of multiplets are observed only in the spot spectrum.</p> + + +<p class="nindc space-above2"> +COBALT (27)</p> + + +<p>The series relations for the arc spectrum of cobalt<a id="FNanchor_324" href="#Footnote_324" class="fnanchor">[324]</a> have been +published by Walters. Cobalt lines are frequent in the solar spectrum, +but as the strongest of them lie near 3500, they cannot be traced in +the spectra of stars. The following multiplets are certainly identified +in the spectrum of the sun: \(^{4}F-^{4}D\), \(^{4}F-^{4}D'\), \(^{4}F-^{4}F''\), +\(^{4}F-^{4}G\), \(^{4}F-^{4}D\), \(^{4}F-^{4}D'\), \(^{4}F'-^{4}F''\), \(^{4}F'-^{4}G\), +\(^{4}P-^{4}D\), \(^{4}P'-^{4}D\), and \(^4P-^4D'\). The incompletely observed +multiplet \(^{4}P'-^{4}D'\) is apparently absent from the solar spectrum.</p> + + +<p class="nindc space-above2"> +NICKEL (28)</p> + + +<p>The series relations for nickel are as yet unpublished. The lines +appear in great numbers in the solar spectrum, but they are not strong +enough to be conspicuous in the spectra of the stars. The line 5476 +appears to have a maximum at \(G_0\), indicating either that it is +an enhanced line of nickel, or that it is blended with the enhanced +line of some other element. The lines 5081, 4714 are strengthened in +low temperature stars, and are probably due to neutral nickel. From +the solar behavior of the lines of this element,<a id="FNanchor_325" href="#Footnote_325" class="fnanchor">[325]</a> the ionization +potential seems to be of the same order as that for cobalt, probably +about 8 volts.</p> + + +<p class="nindc space-above2"> +COPPER (29)</p> + + +<p>Copper is represented in the solar spectrum by the ultimate doublet +3273, 3247 (\(1^{2}S-m^{2}P\)), which is strong. The pair 5700, 5782 +(\(x-1^{2}P\)) is probably also present. The former lines are too far +in the ultra-violet to have been studied in the stars, and the latter +are too faint.</p> + + +<p class="nindc space-above2"> +ZINC (30)</p> + + +<p>The principal singlet \(_1S-_1P\) is at 2138, and has therefore not +been observed in stellar spectra. The \(1^{3}P-1^{3}S\) lines at 4722, +4810, are seen in the stellar sequence, where they appear at \(F_0\), +and have a maximum<a id="FNanchor_326" href="#Footnote_326" class="fnanchor">[326]</a> at \(G_0\).</p> + +<p><span class="pagenum" id="Page_81">[Pg 81]</span></p> + +<p>Two unclassified lines of ionized zinc are mentioned in Fowler’s Report +as lying at 5894, 6214. Neither of these lines can be traced in solar +or stellar spectra.</p> + + +<p class="nindc space-above2"> +GALLIUM (31)</p> + + +<p>The occurrence of gallium in stellar spectra is confined to the +identification of two solar lines by Hartley and Ramage.<a id="FNanchor_327" href="#Footnote_327" class="fnanchor">[327]</a> The +lines in question are at 4033, 4172, and are the ultimate lines of the +element (\(1^{2}P-m^{2}S\)). They are too faint to be studied in the +stars.</p> + + +<p class="nindc space-above2"> +RUBIDIUM (37)</p> + + +<p>The ultimate lines of rubidium have been detected in the sunspot +spectrum,<a id="FNanchor_328" href="#Footnote_328" class="fnanchor">[328]</a> but they are not found in the spectra of the sun or +stars.</p> + + +<p class="nindc space-above2"> +STRONTIUM (38)</p> + + +<p>The element strontium is of great astrophysical importance, owing to +the use of its enhanced lines in the estimation of absolute magnitudes. +The neutral atom is represented in the sun and stars by the ultimate +line (\(_1S-mP\)) 4607, which is first clearly seen<a id="FNanchor_329" href="#Footnote_329" class="fnanchor">[329]</a> at \(F_0\), +and increases progressively in strength with advancing type. It varies +with absolute magnitude, being weakened in stars of high luminosity +later than \(K_0\). Estimates for the intensity of this line are +difficult with small dispersions, as it is blended in cool stars.</p> + + +<p class="nindc space-above2"> +IONIZED STRONTIUM</p> + + +<p>Ionized strontium is represented in stellar spectra by the +\(1^{2}S-m^{2}P\) and the \(1^{2}P-m^{2}S\) series. The former contains +the important absolute magnitude lines 4215, 4077, which are first seen +at about \(A_0\), and reach a maximum<a id="FNanchor_330" href="#Footnote_330" class="fnanchor">[330]</a> near \(K_2\). They appear +to have “abnormal” intensities in certain stars,<a id="FNanchor_331" href="#Footnote_331" class="fnanchor">[331]</a> and in the \(A\) +stars are often the finest and sharpest lines in the spectrum. This +behavior suggests a high-level origin, but “stationary Strontium,” +<span class="pagenum" id="Page_82">[Pg 82]</span> +although suggested by Plaskett<a id="FNanchor_332" href="#Footnote_332" class="fnanchor">[332]</a> as likely to occur, has not yet +been observed.</p> + + +<p class="nindc space-above2"> +YTTRIUM (39)</p> + + +<p>Numerous lines of yttrium<a id="FNanchor_333" href="#Footnote_333" class="fnanchor">[333]</a> are found in the solar spectrum. The +lines of the ionized atom are somewhat stronger than the lines of the +neutral atom. The lines of the neutral element which can be identified +in the solar spectrum are contained in the following table.</p> + +<h2><a id="TABLE_XV">TABLE XV</a></h2> + +<table class="autotable"> +<thead><tr> +<th class="tdc bb bt2 br">Series</th> +<th class="tdc bb bt2 br">Wave-Lenght</th> +<th class="tdc bb bt2 br"> Int. </th> +<th class="tdc bb bt2 br">Attribution</th> +<th class="tdc bb bt2 br"> Int. </th> +<th class="tdc bb bt2">Wave-Lenght</th> +</tr> +</thead> +<tbody><tr> +<td class="tdc br">\(^2D_3-^2P_2\)</td> +<td class="tdc br">3620.94</td> +<td class="tdc br">20</td> +<td class="tdc br">Y?</td> +<td class="tdc br"><span class="tight">00</span></td> +<td class="tdc">3621.110</td> +</tr><tr> +<td class="tdc br">\(^2D_2-^2P_1\)</td> +<td class="tdc br">3592.91</td> +<td class="tdc br">10</td> +<td class="tdc br">Y</td> +<td class="tdc br">0</td> +<td class="tdc">3593.040</td> +</tr><tr> +<td class="tdc br">\(^2D_2-^2P_2\)</td> +<td class="tdc br">3552.69</td> +<td class="tdc br">3</td> +<td class="tdc br"></td> +<td class="tdc br">-</td> +<td class="tdc">-</td> +</tr><tr> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc"></td> +</tr><tr> +<td class="tdc br">\(^2D_3-^2P_2\)</td> +<td class="tdc br">4128.32</td> +<td class="tdc br">30</td> +<td class="tdc br"></td> +<td class="tdc br"><span class="tight">00</span></td> +<td class="tdc">4128.46</td> +</tr><tr> +<td class="tdc br">\(^2D_2-^2P_2\)</td> +<td class="tdc br">4039.83</td> +<td class="tdc br">5</td> +<td class="tdc br">Y</td> +<td class="tdc br"><span class="tight">00</span></td> +<td class="tdc">4040.013</td> +</tr><tr> +<td class="tdc br">\(^2D_2-^2P_1\)</td> +<td class="tdc br">4047.65</td> +<td class="tdc br">8</td> +<td class="tdc br">Y</td> +<td class="tdc br">\(_0N\)</td> +<td class="tdc">4047.823</td> +</tr><tr> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc"></td> +</tr><tr> +<td class="tdc br">\(^2D_3-^2F_4\)</td> +<td class="tdc br">4102.38</td> +<td class="tdc br">20</td> +<td class="tdc br">Y</td> +<td class="tdc br">0</td> +<td class="tdc">4102.541</td> +</tr><tr> +<td class="tdc br">\(^2D_3-^2F_3\)</td> +<td class="tdc br">4167.52</td> +<td class="tdc br">10</td> +<td class="tdc br"></td> +<td class="tdc br"><span class="tight">00</span></td> +<td class="tdc">4167.737</td> +</tr><tr> +<td class="tdc bb br">\(^2D_2-^2F_3\)</td> +<td class="tdc bb br">4077.39</td> +<td class="tdc bb br">20</td> +<td class="tdc bb br">La, Y</td> +<td class="tdc bb br">\(_1Nd\)?</td> +<td class="tdc bb">4077.498</td> +</tr> +</tbody> +</table> + + +<p>The multiplets \(^{2}D-^{2}P\) at 4174, etc., and \(^{2}D-^{2}F\) at 4674, +etc., and the \(^{2}D-^{2}D'\) multiplets, do not appear in the solar +spectrum. None of the above lines is strong enough to be seen in the +spectra of the stars.</p> + + +<p class="nindc space-above2"> +IONIZED YTTRIUM</p> + + +<p><span class="pagenum" id="Page_83">[Pg 83]</span></p> + +<p>Four of the multiplets attributed to ionized yttrium<a id="FNanchor_334" href="#Footnote_334" class="fnanchor">[334]</a> are +satisfactorily identified in the solar spectrum. The wave-lengths and +identifications are contained in <a href="#TABLE_XVI">Table XVI</a>, p. 83. The arrangement is +as in <a href="#TABLE_XI">Table XI</a>.</p> + +<h2><a id="TABLE_XVI">TABLE XVI</a></h2> + +<table class="autotable"> +<thead><tr> +<th class="tdc bb bt2 br">Series</th> +<th class="tdc bb bt2 br">Wave-Lenght</th> +<th class="tdc bb bt2 br"> Int. </th> +<th class="tdc bb bt2 br">Attribution</th> +<th class="tdc bb bt2 br"> Int. </th> +<th class="tdc bb bt2">Wave-Lenght</th> +</tr> +</thead> +<tbody><tr> +<td class="tdc br">*\(^3D_3-^3F_4\)</td> +<td class="tdc br">3710.30</td> +<td class="tdc br">100</td> +<td class="tdc br">Y</td> +<td class="tdc br">3</td> +<td class="tdc">3710.431</td> +</tr><tr> +<td class="tdc br">\(^3D_3-^3F_3\)</td> +<td class="tdc br">3832.87</td> +<td class="tdc br">20</td> +<td class="tdc br"></td> +<td class="tdc br">\(_3N\)</td> +<td class="tdc">3833.026</td> +</tr><tr> +<td class="tdc br">*\(^3D_2-^3F_2\)</td> +<td class="tdc br">3774.33</td> +<td class="tdc br">50</td> +<td class="tdc br">Y</td> +<td class="tdc br">3</td> +<td class="tdc">3774.473</td> +</tr><tr> +<td class="tdc br">\(^3D_3-^3F_2\)</td> +<td class="tdc br">3878.27</td> +<td class="tdc br">4</td> +<td class="tdc br"></td> +<td class="tdc br">1</td> +<td class="tdc">3878.334</td> +</tr><tr> +<td class="tdc br">\(^3D_2-^3F_2\)</td> +<td class="tdc br">3818.37</td> +<td class="tdc br">10</td> +<td class="tdc br">Y</td> +<td class="tdc br">1</td> +<td class="tdc">3818.487</td> +</tr><tr> +<td class="tdc br">*\(^3D_1-^3F_2\)</td> +<td class="tdc br">3788.69</td> +<td class="tdc br">30</td> +<td class="tdc br"></td> +<td class="tdc br">2</td> +<td class="tdc">3788.839</td> +</tr><tr> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc"></td> +</tr><tr> +<td class="tdc br">\(^3D_3-^3D_3\)</td> +<td class="tdc br">3600.72</td> +<td class="tdc br">50</td> +<td class="tdc br">Y</td> +<td class="tdc br">3</td> +<td class="tdc">3600.880</td> +</tr><tr> +<td class="tdc br">\(^3D_2-^3D_3\)</td> +<td class="tdc br">3548.99</td> +<td class="tdc br">20</td> +<td class="tdc br">Y?</td> +<td class="tdc br">2</td> +<td class="tdc">3549.151</td> +</tr><tr> +<td class="tdc br">\(^3D_3-^3D_2\)</td> +<td class="tdc br">3664.59</td> +<td class="tdc br">20</td> +<td class="tdc br">Y</td> +<td class="tdc br">2</td> +<td class="tdc">3664.760</td> +</tr><tr> +<td class="tdc br">\(^3D_2-^3D_2\)</td> +<td class="tdc br">3611.05</td> +<td class="tdc br">30</td> +<td class="tdc br">Y, Mg?</td> +<td class="tdc br">2</td> +<td class="tdc">3611.189</td> +</tr><tr> +<td class="tdc br">\(^3D_1-^3D_2\)</td> +<td class="tdc br">3584.51</td> +<td class="tdc br">10</td> +<td class="tdc br">Y</td> +<td class="tdc br">2</td> +<td class="tdc">3584.660</td> +</tr><tr> +<td class="tdc br">\(^3D_2-^3D_1\)</td> +<td class="tdc br">3628.70</td> +<td class="tdc br">10</td> +<td class="tdc br">Y, Mg?</td> +<td class="tdc br">2</td> +<td class="tdc">3628.847</td> +</tr><tr> +<td class="tdc br">\(^3D_1-^3D_1\)</td> +<td class="tdc br">3601.91</td> +<td class="tdc br">20</td> +<td class="tdc br">Y</td> +<td class="tdc br">1</td> +<td class="tdc">3602.060</td> +</tr><tr> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc"></td> +</tr><tr> +<td class="tdc br">\(^3D_3-^3P_2\)</td> +<td class="tdc br">4309.61</td> +<td class="tdc br">20</td> +<td class="tdc br"></td> +<td class="tdc br">1</td> +<td class="tdc">4309.792</td> +</tr><tr> +<td class="tdc br">\(^3D_2-^3P_2\)</td> +<td class="tdc br">4235.71</td> +<td class="tdc br">6</td> +<td class="tdc br"></td> +<td class="tdc br">0</td> +<td class="tdc">4235.894</td> +</tr><tr> +<td class="tdc br">\(^3D_1-^3P_2\)</td> +<td class="tdc br">4199.283</td> +<td class="tdc br">3</td> +<td class="tdc br"></td> +<td class="tdc br"><span class="tight">00</span></td> +<td class="tdc">4199.434</td> +</tr><tr> +<td class="tdc br">\(^3D_2-^3P_1\)</td> +<td class="tdc br">4398.03</td> +<td class="tdc br">15</td> +<td class="tdc br">In zircon <a href="#ii">*</a></td> +<td class="tdc br">1</td> +<td class="tdc">4398.178</td> +</tr><tr> +<td class="tdc br">\(^3D_1-^3P_1\)</td> +<td class="tdc br">4358.72</td> +<td class="tdc br">8</td> +<td class="tdc br">Y-Zr</td> +<td class="tdc br">0</td> +<td class="tdc">4358.879</td> +</tr><tr> +<td class="tdc br">\(^3D_1-^3P_0\)</td> +<td class="tdc br">4422.60</td> +<td class="tdc br">10</td> +<td class="tdc br">Fe, Y</td> +<td class="tdc br">3</td> +<td class="tdc">4422.741</td> +</tr><tr> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc"></td> +</tr><tr> +<td class="tdc br">\(^3F_4-^3F'_4\)</td> +<td class="tdc br">5087.42</td> +<td class="tdc br">10</td> +<td class="tdc br">Y?</td> +<td class="tdc br">1</td> +<td class="tdc">5087.601</td> +</tr><tr> +<td class="tdc br">\(^3F_3-^3F'_4\)</td> +<td class="tdc br">4982.12</td> +<td class="tdc br">3</td> +<td class="tdc br"></td> +<td class="tdc br"><span class="tight">000</span></td> +<td class="tdc">4982.319</td> +</tr><tr> +<td class="tdc br">\(^3F_4-^3F'_3\)</td> +<td class="tdc br">5320.77</td> +<td class="tdc br">1</td> +<td class="tdc br"></td> +<td class="tdc br">-</td> +<td class="tdc">-</td> +</tr><tr> +<td class="tdc br">\(^3F_3-^3F'_3\)</td> +<td class="tdc br">5205.71</td> +<td class="tdc br">10</td> +<td class="tdc br">Y</td> +<td class="tdc br">0</td> +<td class="tdc">5205.897</td> +</tr><tr> +<td class="tdc br">\(^3F_2-^3F'_3\)</td> +<td class="tdc br">5119.10</td> +<td class="tdc br">3</td> +<td class="tdc br"></td> +<td class="tdc br"><span class="tight">00</span></td> +<td class="tdc">5119.292</td> +</tr><tr> +<td class="tdc br">\(^3F_3-^3F'_2\)</td> +<td class="tdc br">5289.81</td> +<td class="tdc br">2</td> +<td class="tdc br"></td> +<td class="tdc br"><span class="tight">000</span></td> +<td class="tdc">5289.988</td> +</tr><tr> +<td class="tdc bb br">\(^3F_2-^3F'_2\)</td> +<td class="tdc bb br">5200.41</td> +<td class="tdc bb br">8</td> +<td class="tdc bb br">V</td> +<td class="tdc bb br">0</td> +<td class="tdc bb">5200.590</td> +</tr> +</tbody> +</table> + +<p class="nindc"><a id="ii">*</a> But not Zr.</p> + + + +<p class="nindc space-above2"> +ZIRCONIUM (40)</p> + + +<p>The ultimate lines of the zirconium atom<a id="FNanchor_335" href="#Footnote_335" class="fnanchor">[335]</a> are all found in the +solar spectrum, far into the ultra-violet.</p> + +<p>The bands in the spectra of stars of Class \(S\) are found to correspond +with those of ZrO₂, zirconium oxide.<a id="FNanchor_336" href="#Footnote_336" class="fnanchor">[336]</a> A comparison +<span class="pagenum" id="Page_84">[Pg 84]</span> +of the furnace spectrum of zirconium oxide with that of titanium oxide, which produces +the characteristic flutings in Class \(M\), indicates that titanium oxide +persists to lower temperatures.<a id="FNanchor_337" href="#Footnote_337" class="fnanchor">[337]</a> It is of interest to note that +the only oxides, other than water, which have been detected in stellar +spectra, are those of elements in the fourth column of the periodic +table, namely carbon, titanium and zirconium. Probably this has a +chemical interpretation. The presence of silicon dioxide SiO₂ has not +been detected, although it might be anticipated.</p> + + +<p class="nindc space-above2"> +NIOBIUM (41)</p> + + +<p>Rowland identifies some of the lines associated with niobium in the +solar spectrum. The series relations are unknown, and the lines are too +faint to be detected in stellar spectra.</p> + + +<p class="nindc space-above2"> +MOLYBDENUM (42)</p> + + +<p>All the ultimate lines of molybdenum are present in the solar spectrum. +They are too faint to be detected in the stars. The spectrum has been +analyzed into series by Kiess,<a id="FNanchor_338" href="#Footnote_338" class="fnanchor">[338]</a> and by Catalan.<a id="FNanchor_339" href="#Footnote_339" class="fnanchor">[339]</a></p> + + +<p class="nindc space-above2"> +RUTHENIUM (44) RHODIUM (45) PALLADIUM (46)</p> + + +<p>The strongest lines in the spectra of the three lighter platinum metals +are all present in the solar spectrum,<a id="FNanchor_340" href="#Footnote_340" class="fnanchor">[340]</a> but are too faint to be +traced in the spectra of stars. Series relations are as yet unknown. +The heavier platinum metals, osmium (76), iridium (77), and platinum +(78), are not certainly found in the solar spectrum.</p> + + +<p class="nindc space-above2"> +SILVER (47)</p> + + +<p><span class="pagenum" id="Page_85">[Pg 85]</span></p> + +<p>The ultimate (\(1^{2}S-m^{2}P\)) lines of silver are at 3281 and 3383. +They are both faintly present in the solar spectrum. The doublet at +4669, 4476 (\(1^{2}P-m^{2}S\)) is also probably present in the spectrum +of the sun. The lines cannot be traced in stellar spectra.</p> + + +<p class="nindc space-above2"> +TIN (50)</p> + +<p>A line of neutral tin was reported by Lunt<a id="FNanchor_341" href="#Footnote_341" class="fnanchor">[341]</a> in the spectrum of +\(\alpha\) Scorpii. Series relations are as yet unknown. In view of the +absence of identifications of related lines, the attribution cannot be +regarded as very certain. The strongest line in the spectrum of ionized +tin is stated by the same investigator to lie at 4585.80. This line is +either absent from or exceedingly weak in the solar spectrum.</p> + + +<p class="nindc space-above2"> +BARIUM (56)</p> + + +<p>Neutral barium is not certainly present in stellar spectra. The first +two ultimate lines (\(_1S-mP\)) fall in the red and the ultra-violet +respectively, and would therefore escape notice in the stars. No lines +of corresponding wave-length appear in Rowland’s table, but they are +found in sunspots.<a id="FNanchor_342" href="#Footnote_342" class="fnanchor">[342]</a> The \(P-P'\) groups are also absent from the +solar spectrum.</p> + +<p>The strength of the barium lines in the sun has been thought by Russell +to be abnormal, and the question has been considered by several +investigators.<a id="FNanchor_343" href="#Footnote_343" class="fnanchor">[343]</a><a id="FNanchor_344" href="#Footnote_344" class="fnanchor">[344]</a><a id="FNanchor_345" href="#Footnote_345" class="fnanchor">[345]</a></p> + + +<p class="nindc space-above2"> +IONIZED BARIUM</p> + + +<p>Ionized barium is represented by the \(1^{2}P-m^{2}D\) lines which are +present, though weak, in the sun, and by the \(1^{2}S-m^{2}P\) lines, +which appear<a id="FNanchor_346" href="#Footnote_346" class="fnanchor">[346]</a> at \(A_3\), and increase in intensity for all cooler +stars. The \(1^{2}S-m^{2}P\) line is at 4555, and its behavior is +difficult to trace, as it is much blended.</p> + + +<p class="nindc space-above2"> +THE RARE EARTHS (57-71)</p> + + +<p>The spectra of the rare earths are so rich in lines that spurious +identifications with lines in stellar spectra are often likely to +occur. Numerous attributions to lanthanum (57), cerium (58), and +<span class="pagenum" id="Page_86">[Pg 86]</span> +neodymium (60) are given in Rowland’s table. The occurrence of some of +these elements has also been definitely established in the spectra of +certain stars. Kiess<a id="FNanchor_347" href="#Footnote_347" class="fnanchor">[347]</a> has demonstrated the presence of europium +(63) and of terbium (65) in \(\alpha\) Canum Venaticorum. Numerous +lines, identified with those of rare earth elements, are reported by +Mitchell<a id="FNanchor_348" href="#Footnote_348" class="fnanchor">[348]</a>in the chromospheric spectrum.</p> + +<p>If the lines in the chromosphere and the \(A\) star are indeed derived +from the rare earths, the atoms concerned must be at least singly +ionized. No series relations have as yet been published for any rare +earth element, excepting a short list of relative term values for +lanthanum.<a id="FNanchor_349" href="#Footnote_349" class="fnanchor">[349]</a> From analogy with the previous long period it would +seem unlikely that the first ionization potential of these atoms can be +as great as 13 volts, the value which would be required if the lines +have a maximum intensity at \(A_0\).</p> + + +<p class="nindc space-above2"> +LEAD (82)</p> + + +<p>A single line is attributed to lead in Rowland’s table.</p> + + +<p class="nindc space-above2"> +RADIUM (88)</p> + + +<p>Giebeler and Küstner<a id="FNanchor_350" href="#Footnote_350" class="fnanchor">[350]</a> suggested the occurrence of radium lines in +the chromosphere. The identification was discussed by Dyson<a id="FNanchor_351" href="#Footnote_351" class="fnanchor">[351]</a> and by +Mitchell.<a id="FNanchor_352" href="#Footnote_352" class="fnanchor">[352]</a> In the light of later knowledge it appears improbable +that an element so heavy, and terrestrially so rare,<a id="FNanchor_353" href="#Footnote_353" class="fnanchor">[353]</a> would be +present in the sun at sufficient heights and in great enough quantity +to appear in the flash spectrum. The identification is probably to be +regarded as spurious.</p> + + +<p class="nindc space-above2"> +ELEMENTS NOT DETECTED IN STELLAR SPECTRA</p> + + +<p>The table which follows contains a list of elements which are absent, +or of doubtful occurrence. The rare earths are omitted from the list.</p> + +<p><span class="pagenum" id="Page_87">[Pg 87]</span></p> + +<p>The elements marked “doubtful” in the list are those for which +coincidences with very faint solar lines occur.<a id="FNanchor_354" href="#Footnote_354" class="fnanchor">[354]</a> Twelve out of +the twenty-nine elements enumerated are halogens, inert gases, or +metalloids, and it is significant that all the elements of these groups +are absent, with the sole exception of helium.</p> + +<table class="autotable"> +<thead><tr> +<th class="tdc">At. No. </th> +<th class="tdc">Element </th> +<th class="tdc">Remark </th> +<th class="tdc">At. No. </th> +<th class="tdc">Element </th> +<th class="tdc"> Remark</th> +</tr> +</thead> +<tbody><tr> +<td class="tdc">4</td> +<td class="tdl">Beryllium</td> +<td class="tdl">Doubtful</td> +<td class="tdc">53</td> +<td class="tdl">Iodine</td> +<td class="tdl">Absent</td> +</tr><tr> +<td class="tdc">5</td> +<td class="tdl">Boron</td> +<td class="tdl">Absent</td> +<td class="tdc">54</td> +<td class="tdl">Xenon</td> +<td class="tdl">Absent</td> +</tr><tr> +<td class="tdc">9</td> +<td class="tdl">Fluorine</td> +<td class="tdl">Absent</td> +<td class="tdc">73</td> +<td class="tdl">Tantalum</td> +<td class="tdl">Doubtful</td> +</tr><tr> +<td class="tdc">10</td> +<td class="tdl">Neon</td> +<td class="tdl">Absent</td> +<td class="tdc">74</td> +<td class="tdl">Tungsten</td> +<td class="tdl">Doubtful</td> +</tr><tr> +<td class="tdc">15</td> +<td class="tdl">Phosphorus</td> +<td class="tdl">Absent</td> +<td class="tdc">76</td> +<td class="tdl">Osmium</td> +<td class="tdl">Doubtful</td> +</tr><tr> +<td class="tdc">17</td> +<td class="tdl">Chlorine</td> +<td class="tdl">Absent</td> +<td class="tdc">77</td> +<td class="tdl">Iridium</td> +<td class="tdl">Doubtful</td> +</tr><tr> +<td class="tdc">18</td> +<td class="tdl">Argon</td> +<td class="tdl">Absent</td> +<td class="tdc">78</td> +<td class="tdl">Platinum</td> +<td class="tdl">Doubtful</td> +</tr><tr> +<td class="tdc">32</td> +<td class="tdl">Germanium</td> +<td class="tdl">Doubtful</td> +<td class="tdc">79</td> +<td class="tdl">Gold</td> +<td class="tdl">Absent</td> +</tr><tr> +<td class="tdc">33</td> +<td class="tdl">Arsenic</td> +<td class="tdl">Absent</td> +<td class="tdc">80</td> +<td class="tdl">Mercury</td> +<td class="tdl">Doubtful</td> +</tr><tr> +<td class="tdc">34</td> +<td class="tdl">Selenium</td> +<td class="tdl">Absent</td> +<td class="tdc">81</td> +<td class="tdl">Thallium</td> +<td class="tdl">Doubtful</td> +</tr><tr> +<td class="tdc">35</td> +<td class="tdl">Bromine</td> +<td class="tdl">Absent</td> +<td class="tdc">83</td> +<td class="tdl">Bismuth</td> +<td class="tdl">Doubtful</td> +</tr><tr> +<td class="tdc">36</td> +<td class="tdl">Krypton</td> +<td class="tdl">Absent</td> +<td class="tdc">86</td> +<td class="tdl">Radon</td> +<td class="tdl">Absent</td> +</tr><tr> +<td class="tdc">49</td> +<td class="tdl">Indium</td> +<td class="tdl">Doubtful</td> +<td class="tdc">90</td> +<td class="tdl">Thorium</td> +<td class="tdl">Doubtful</td> +</tr><tr> +<td class="tdc">51</td> +<td class="tdl">Antimony</td> +<td class="tdl">Absent</td> +<td class="tdc">92</td> +<td class="tdl">Uranium</td> +<td class="tdl">Doubtful</td> +</tr><tr> +<td class="tdc">52</td> +<td class="tdl">Tellurium</td> +<td class="tdl">Absent</td> +<td class="tdc"></td> +<td class="tdl"></td> +<td class="tdl"></td> +</tr> +</tbody> +</table> + + + +<div class="footnotes"><h3>FOOTNOTES:</h3> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_125" href="#FNanchor_125" class="label">[125]</a> +M. N. R. A. S., 83, 166, 1923; <i>ibid.</i>, 84, 368, +1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_126" href="#FNanchor_126" class="label">[126]</a> +Ap. J., 61, 38, 1925.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_127" href="#FNanchor_127" class="label">[127]</a> +Wright, Lick Pub., 13, 242, 1918.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_128" href="#FNanchor_128" class="label">[128]</a> +A. Fowler, M. N. R. A. S., 80, 692, 1920.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_129" href="#FNanchor_129" class="label">[129]</a> +H. A., 91, 7, 1918.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_130" href="#FNanchor_130" class="label">[130]</a> +Fairfield, H. C. 264, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_131" href="#FNanchor_131" class="label">[131]</a> +H. C. 258, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_132" href="#FNanchor_132" class="label">[132]</a> +<i>Ibid.</i></p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_133" href="#FNanchor_133" class="label">[133]</a> +Payne, Proc. N. Ac. Sci., 11, 192, 1925; Chapter XIII, +<a href="#Page_188">p. 188</a>.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_134" href="#FNanchor_134" class="label">[134]</a> +Nature, 114, 86, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_135" href="#FNanchor_135" class="label">[135]</a> +Personal letter.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_136" href="#FNanchor_136" class="label">[136]</a> +Chapter IV, <a href="#Page_51">p. 51</a>.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_137" href="#FNanchor_137" class="label">[137]</a> +Mt. W. Contr. 262, 1922.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_138" href="#FNanchor_138" class="label">[138]</a> +Fairfield, H. C. 264, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_139" href="#FNanchor_139" class="label">[139]</a> +Lindblad, Ap. J., 59, 305, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_140" href="#FNanchor_140" class="label">[140]</a> +Chapter XII, <a href="#Page_168">p. 168</a>.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_141" href="#FNanchor_141" class="label">[141]</a> +Ap. J., 29, 100, 1909.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_142" href="#FNanchor_142" class="label">[142]</a> +Ap. J., 60, 1, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_143" href="#FNanchor_143" class="label">[143]</a> +Atlas, p. 85, 1892.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_144" href="#FNanchor_144" class="label">[144]</a> +Wright, Nature, 109, 810, 1920.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_145" href="#FNanchor_145" class="label">[145]</a> +Chapter III, <a href="#Page_43">p. 43</a>.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_146" href="#FNanchor_146" class="label">[146]</a> +Pub. A. S. P., 32, 155, 1920.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_147" href="#FNanchor_147" class="label">[147]</a> +Mitchell, Ap. J., 38, 431, 1913.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_148" href="#FNanchor_148" class="label">[148]</a> +Phil. Trans., 197A, 381, 1901.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_149" href="#FNanchor_149" class="label">[149]</a> +C. R., 114, 578, 1892.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_150" href="#FNanchor_150" class="label">[150]</a> +Pub. Obs. Mich., 3, 256, 1923.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_151" href="#FNanchor_151" class="label">[151]</a> +Payne, H. C. 256, 1924; <i>ibid.</i>, 263, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_152" href="#FNanchor_152" class="label">[152]</a> +Henry Draper Catalogue; criterion of class.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_153" href="#FNanchor_153" class="label">[153]</a> +Lyman, Phys. Rev., 21, 202, 1923.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_154" href="#FNanchor_154" class="label">[154]</a> +Payne, Nature, 113, 783, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_155" href="#FNanchor_155" class="label">[155]</a> +Mitchell, Ap. J., 38, 407, 1913.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_156" href="#FNanchor_156" class="label">[156]</a> +H. C. 263, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_157" href="#FNanchor_157" class="label">[157]</a> +Pub. Dom. Ap. Obs., 1, 335, 1922.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_158" href="#FNanchor_158" class="label">[158]</a> +Mt. W. Contr. 236, 1922.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_159" href="#FNanchor_159" class="label">[159]</a> +Mt. W. Contr. p. 160, 236, 1922.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_160" href="#FNanchor_160" class="label">[160]</a> +De Gramont, C. R., 171, 1106, 1920.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_161" href="#FNanchor_161" class="label">[161]</a> +Naturwiss., 12, 139, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_162" href="#FNanchor_162" class="label">[162]</a> +Quoted by de Forcrand.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_163" href="#FNanchor_163" class="label">[163]</a> +C. R., 178, 1868, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_164" href="#FNanchor_164" class="label">[164]</a> +A. Fowler, Proc. Roy. Soc., 105A, 299, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_165" href="#FNanchor_165" class="label">[165]</a> +H. H. Plaskett, Pub. Dom. Ap. Obs., 1, 351, 1922.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_166" href="#FNanchor_166" class="label">[166]</a> +Payne, H. C. 256, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_167" href="#FNanchor_167" class="label">[167]</a> +Wright, Lick Pub., 13, 193, 1918.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_168" href="#FNanchor_168" class="label">[168]</a> +W. W. Campbell, Ast. and Ap., 13, 448, 1894.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_169" href="#FNanchor_169" class="label">[169]</a> +J. S. Plaskett, Pub. Dom. Ap. Obs., 2, 287, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_170" href="#FNanchor_170" class="label">[170]</a> +T. R. Merton, Proc. Roy. Soc., 91A, 498, 1915.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_171" href="#FNanchor_171" class="label">[171]</a> +Wright, Lick Pub., 13, 193, 1918.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_172" href="#FNanchor_172" class="label">[172]</a> +T. R. Merton, Proc. Roy. Soc., 91A, 498, 1915.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_173" href="#FNanchor_173" class="label">[173]</a> +A. Fowler, Proc. Roy. Soc., 105A, 299, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_174" href="#FNanchor_174" class="label">[174]</a> +H. C. 263, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_175" href="#FNanchor_175" class="label">[175]</a> +R. H. Fowler and Milne, M. N. R. A. S., 84, 502, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_176" href="#FNanchor_176" class="label">[176]</a> +D. R. Hartree, Proc. Camb. Phil. Soc., 22, 409, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_177" href="#FNanchor_177" class="label">[177]</a> +R. H. Fowler and Milne, M. N. R. A. S., 84, 502, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_178" href="#FNanchor_178" class="label">[178]</a> +M. N. R. A. S., 77, 511, 1917.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_179" href="#FNanchor_179" class="label">[179]</a> +Wright, Lick Pub., 13, 193, 1918.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_180" href="#FNanchor_180" class="label">[180]</a> +Mulliken, Nature, 114, 858, 1924; Birge, Phys. Rev. 23, +294, 1924; Freundlich and Hocheim, Zeit. f. Phys., 26, 102, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_181" href="#FNanchor_181" class="label">[181]</a> +Kayser, Handbuch der Spektroskopie, Vol. VII, 132, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_182" href="#FNanchor_182" class="label">[182]</a> +Evershed, Kod. Bul. 36, 1913.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_183" href="#FNanchor_183" class="label">[183]</a> +Lindblad, Mt. W. Contr. 228, 1922.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_184" href="#FNanchor_184" class="label">[184]</a> +Shapley and Lindblad, H. C. 228, 1921.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_185" href="#FNanchor_185" class="label">[185]</a> +Lindblad, Mt. W. Contr. 228, 1922.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_186" href="#FNanchor_186" class="label">[186]</a> +Shapley, H. B. 805, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_187" href="#FNanchor_187" class="label">[187]</a> +Mt. W. Contr. 228, 1922.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_188" href="#FNanchor_188" class="label">[188]</a> +L. O. B. 329, 1919.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_189" href="#FNanchor_189" class="label">[189]</a> +Rufus, Pub. Obs. Mich., 3, 257, 1923.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_190" href="#FNanchor_190" class="label">[190]</a> +A. Fowler, M. N. R. A. S., 70, 176, 1909.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_191" href="#FNanchor_191" class="label">[191]</a> +Evershed, M. N. R. A. S., 68, 16, 1907.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_192" href="#FNanchor_192" class="label">[192]</a> +Pluvinel and Baldet, Ap. J., 34, 89, 1907.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_193" href="#FNanchor_193" class="label">[193]</a> +Merton and Johnson, Proc. Roy. Soc., 103A, 383, 1923.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_194" href="#FNanchor_194" class="label">[194]</a> +A. Fowler, M. N. R. A. S., 70, 176, 1909.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_195" href="#FNanchor_195" class="label">[195]</a> +Hale, Ellerman, and Parkhurst, Yerkes Pub., 2, 253, +1903.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_196" href="#FNanchor_196" class="label">[196]</a> +Shane, L. O. B. 329, 1919.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_197" href="#FNanchor_197" class="label">[197]</a> +M. N. R. A. S., 70, 176 and 484, 1909.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_198" href="#FNanchor_198" class="label">[198]</a> +Strutt, Proc. Phys. Soc. Lond., 23, 147, 1911.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_199" href="#FNanchor_199" class="label">[199]</a> +Stead, Phil. Mag., 22, 727, 1911.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_200" href="#FNanchor_200" class="label">[200]</a> +A. Fowler, M. N. R. A. S., 70, 176 and 484, 1909.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_201" href="#FNanchor_201" class="label">[201]</a> +C. R., 177, 1205, 1923.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_202" href="#FNanchor_202" class="label">[202]</a> +Pluvinel and Baldet, Ap. J., 34, 89, 1911.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_203" href="#FNanchor_203" class="label">[203]</a> +M. N. R. A. S., 76, 640, 1916.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_204" href="#FNanchor_204" class="label">[204]</a> +Chapter XIV, <a href="#Page_167">p. 167</a>.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_205" href="#FNanchor_205" class="label">[205]</a> +Fowler, Report on Series in Line Spectra, 164, 1922.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_206" href="#FNanchor_206" class="label">[206]</a> +Smyth, Proc. Roy. Soc., 103A, 121, 1923.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_207" href="#FNanchor_207" class="label">[207]</a> +Vegard, Videns. Skr., 1, nos. 8, 9, 10, 1923, where +previous work is summarized.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_208" href="#FNanchor_208" class="label">[208]</a> +Vegard, Proc. Amst. Ac., 27, 1 and 2, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_209" href="#FNanchor_209" class="label">[209]</a> +A. Fowler, M. N. R. A. S., 70, 484, 1909.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_210" href="#FNanchor_210" class="label">[210]</a> +See <a href="#Page_61">p. 61</a>.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_211" href="#FNanchor_211" class="label">[211]</a> +Vegard, Proc. Amst. Ac., 27, 1 and 2, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_212" href="#FNanchor_212" class="label">[212]</a> +Proc. Roy. Soc., 106A, 138, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_213" href="#FNanchor_213" class="label">[213]</a> +Nature, 115, 382, 1925.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_214" href="#FNanchor_214" class="label">[214]</a> +Lord Rayleigh, Proc. Roy. Soc., 100A, 367, 1921; +<i>ibid.</i> 101A, 312, 1922.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_215" href="#FNanchor_215" class="label">[215]</a> +A. Fowler, Proc. Roy. Soc., 107A, 31, 1925.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_216" href="#FNanchor_216" class="label">[216]</a> +Payne, H. C. 256, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_217" href="#FNanchor_217" class="label">[217]</a> +Ruark, Mohler, Foote, and Chenault, Bur. Stan. Sci. Pap. +480, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_218" href="#FNanchor_218" class="label">[218]</a> +Proc. Roy. Soc., 82A, 532, 1909.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_219" href="#FNanchor_219" class="label">[219]</a> +Pub. Solar Phys. Comm., 1910.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_220" href="#FNanchor_220" class="label">[220]</a> +Payne, H. C. 256, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_221" href="#FNanchor_221" class="label">[221]</a> +H. H. Plaskett, Pub. Dom. Ap. Obs., 1, 356, 1922.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_222" href="#FNanchor_222" class="label">[222]</a> +Paddock, Pub. A. S. P., 31, 54, 1919.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_223" href="#FNanchor_223" class="label">[223]</a> +Plaskett, J. R. A. S. Can., 12, 350, 1918.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_224" href="#FNanchor_224" class="label">[224]</a> +Baxandall, Pub. A. S. P., 311 297, 1919.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_225" href="#FNanchor_225" class="label">[225]</a> +Wright, M. N. R. A. S., 81, 181, 1920.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_226" href="#FNanchor_226" class="label">[226]</a> +<i>Ibid.</i> Pub. A. S. P., 32, 276, 1920.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_227" href="#FNanchor_227" class="label">[227]</a> +Stratton, M. N. R. A. S., 79, 366, 1919.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_228" href="#FNanchor_228" class="label">[228]</a> +Hopfield, Ap. J., 59, 114, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_229" href="#FNanchor_229" class="label">[229]</a> +Runge and Paschen, Wied. An., 61, 641, 1897.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_230" href="#FNanchor_230" class="label">[230]</a> +Curtis and Burns, unpub.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_231" href="#FNanchor_231" class="label">[231]</a> +A. Fowler, Report, 167, 1922.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_232" href="#FNanchor_232" class="label">[232]</a> +<i>Ibid.</i></p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_233" href="#FNanchor_233" class="label">[233]</a> +An. Cape Obs., 10, 5B, 1906.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_234" href="#FNanchor_234" class="label">[234]</a> +Payne, H. C. 256, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_235" href="#FNanchor_235" class="label">[235]</a> +Pub. Dom. Ap. Obs., 1, 325, 1922.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_236" href="#FNanchor_236" class="label">[236]</a> +Henry Draper Catalogue, H. A., 91, 1918.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_237" href="#FNanchor_237" class="label">[237]</a> +M. N. R. A. S., 77, 511, 1917.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_238" href="#FNanchor_238" class="label">[238]</a> +Wright, Lick Pub., 13, 193, 1918.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_239" href="#FNanchor_239" class="label">[239]</a> +H. H. Plaskett, Pub. Dom. Ap. Obs., 1, 325, 1922.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_240" href="#FNanchor_240" class="label">[240]</a> +Payne, H. C. 256, 1924; Proc. N. Ac. Sci., 10, 322, +1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_241" href="#FNanchor_241" class="label">[241]</a> +R. H. Fowler and Milne, M. N. R. A. S., 84, 499, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_242" href="#FNanchor_242" class="label">[242]</a> +Cortie, Ap. J., 28, 379, 1908.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_243" href="#FNanchor_243" class="label">[243]</a> +A. Fowler, M. N. R. A. S., 67, 530, 1907.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_244" href="#FNanchor_244" class="label">[244]</a> +Proc. Roy. Soc., 93A, 577, 1917.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_245" href="#FNanchor_245" class="label">[245]</a> +Riesenfeld and Beja, Medd. Vetens. Nobelinst., 6, 8, +1923.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_246" href="#FNanchor_246" class="label">[246]</a> +Menzel, H. C. 258, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_247" href="#FNanchor_247" class="label">[247]</a> +Heger, L. O. B. 326, 1918.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_248" href="#FNanchor_248" class="label">[248]</a> +Heger, L. O. B. 337, 1922.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_249" href="#FNanchor_249" class="label">[249]</a> +Luyten, Pub. A. S. P., 35, 175, 1923.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_250" href="#FNanchor_250" class="label">[250]</a> +Menzel, H. C. 258, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_251" href="#FNanchor_251" class="label">[251]</a> +de Gramont, C. R., 171, 1106, 1920.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_252" href="#FNanchor_252" class="label">[252]</a> +H. H. Plaskett, Pub. Som. Ap. Obs., 1, 325, 1922.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_253" href="#FNanchor_253" class="label">[253]</a> +Menzel, H. C. 258, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_254" href="#FNanchor_254" class="label">[254]</a> +H. H. Plaskett, Pub. Dom. Ap. Obs., 1, 325,1922.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_255" href="#FNanchor_255" class="label">[255]</a> +Proc. Roy. Soc., 80A, 218, 1907.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_256" href="#FNanchor_256" class="label">[256]</a> +Phil. Trans., 209A, 447, 1909.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_257" href="#FNanchor_257" class="label">[257]</a> +M. N. R. A. S., 67, 530, 1908.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_258" href="#FNanchor_258" class="label">[258]</a> +R. H. Fowler and Milne, M. N. R. A. S., 83, 403, 1923.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_259" href="#FNanchor_259" class="label">[259]</a> +Menzel, H. C. 258, 1924; p. 122.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_260" href="#FNanchor_260" class="label">[260]</a> +Adams and Joy, Pub. A. S. P., 36, 142, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_261" href="#FNanchor_261" class="label">[261]</a> +Paschen, An. d. Phys., 71, 151, 1923.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_262" href="#FNanchor_262" class="label">[262]</a> +Payne, H. C. 252, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_263" href="#FNanchor_263" class="label">[263]</a> +Bakerian Lecture, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_264" href="#FNanchor_264" class="label">[264]</a> +King, Pub. A. S. P., 33, 106, 1921.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_265" href="#FNanchor_265" class="label">[265]</a> +de Gramont, C. R., 171 1106, 1920.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_266" href="#FNanchor_266" class="label">[266]</a> +Payne, H. C. 252, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_267" href="#FNanchor_267" class="label">[267]</a> +<a href="#Page_169">P. 169</a>.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_268" href="#FNanchor_268" class="label">[268]</a> +Payne, H. C. 252, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_269" href="#FNanchor_269" class="label">[269]</a> +Bakerian Lecture, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_270" href="#FNanchor_270" class="label">[270]</a> +Payne, H. C. 263, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_271" href="#FNanchor_271" class="label">[271]</a> +Hopfield, Nature, 112, 437, 1923.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_272" href="#FNanchor_272" class="label">[272]</a> +Proc. Roy. Soc., 80A, 50, 1907.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_273" href="#FNanchor_273" class="label">[273]</a> +H. C. 256, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_274" href="#FNanchor_274" class="label">[274]</a> +M. N. R. A. S., 84, 499, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_275" href="#FNanchor_275" class="label">[275]</a> +Fowler, Report on Series in Line Spectra, 1922.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_276" href="#FNanchor_276" class="label">[276]</a> +Curtis and Burns, unpub.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_277" href="#FNanchor_277" class="label">[277]</a> +Personal letter.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_278" href="#FNanchor_278" class="label">[278]</a> +Russell and Saunders, Ap. J., 61, 38, 1925.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_279" href="#FNanchor_279" class="label">[279]</a> +Menzel, H. C. 258, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_280" href="#FNanchor_280" class="label">[280]</a> +<i>Ibid.</i></p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_281" href="#FNanchor_281" class="label">[281]</a> +Adams and Joy, Pub. A. S. P., 36, 142, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_282" href="#FNanchor_282" class="label">[282]</a> +Ap. J., 19, 268, 1904.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_283" href="#FNanchor_283" class="label">[283]</a> +Lee, Ap. J., 37, 1, 1913.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_284" href="#FNanchor_284" class="label">[284]</a> +Pub. Dom. Ap. Obs., 2, 16, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_285" href="#FNanchor_285" class="label">[285]</a> +Heger, L. O. B. 326, 1918; <i>ibid.</i> 337, 1922.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_286" href="#FNanchor_286" class="label">[286]</a> +Rufus, J. R. A. S. Can., 14, 139, 1920.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_287" href="#FNanchor_287" class="label">[287]</a> +J. S. Plaskett, Pub. Dom. Ap. Obs., 2, 344, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_288" href="#FNanchor_288" class="label">[288]</a> +Russell, Mt. W. Contr., in press.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_289" href="#FNanchor_289" class="label">[289]</a> +J. Op. Soc. Am., 9, 355, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_290" href="#FNanchor_290" class="label">[290]</a> +Mt. W. Contr., in press.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_291" href="#FNanchor_291" class="label">[291]</a> +J. Op. Soc. Am., 8, 609, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_292" href="#FNanchor_292" class="label">[292]</a> +Payne, Proc. N. Ac. Sci., 11, 192, 1925.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_293" href="#FNanchor_293" class="label">[293]</a> +Menzel, H. C. 258, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_294" href="#FNanchor_294" class="label">[294]</a> +Chapter VII, <a href="#Page_113">p. 113</a>.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_295" href="#FNanchor_295" class="label">[295]</a> +Maury, H. A., 28, 79, 1900.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_296" href="#FNanchor_296" class="label">[296]</a> +Russell, Mt. W. Contr., in press.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_297" href="#FNanchor_297" class="label">[297]</a> +H. C. 258, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_298" href="#FNanchor_298" class="label">[298]</a> +Chapter IX, <a href="#Page_123">p. 123</a>.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_299" href="#FNanchor_299" class="label">[299]</a> +<i>loc. cit.</i></p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_300" href="#FNanchor_300" class="label">[300]</a> +A. Fowler, Proc. Roy. Soc., 73A, 219, 1904; M. N. R. A. +S., 69, 508, 1909.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_301" href="#FNanchor_301" class="label">[301]</a> +Hale, Adams and Gale, Ap. J., 24, 185, 1906; Hale and +Adams, <i>ibid.</i>, 25, 75, 1907.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_302" href="#FNanchor_302" class="label">[302]</a> +Rep. of Spectral Class. Comm., I. A. U., 1925.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_303" href="#FNanchor_303" class="label">[303]</a> +W. F. Meggers, J. Wash. Ac. Sci., 13, 317, 1923; +<i>ibid.</i>, 14, 151, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_304" href="#FNanchor_304" class="label">[304]</a> +Menzel, H. C. 258, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_305" href="#FNanchor_305" class="label">[305]</a> +Ap. J., 25, 235, 1907.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_306" href="#FNanchor_306" class="label">[306]</a> +J. Op. Soc. Am., 9, 355, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_307" href="#FNanchor_307" class="label">[307]</a> +Catalan, An. Soc. Espan. Fis. y Quim., 21, 84, 1923.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_308" href="#FNanchor_308" class="label">[308]</a> +Russell, Mt. W. Contr., in press.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_309" href="#FNanchor_309" class="label">[309]</a> +Chapter VIII, <a href="#Page_124">p. 124</a>.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_310" href="#FNanchor_310" class="label">[310]</a> +Menzel, H. C. 258, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_311" href="#FNanchor_311" class="label">[311]</a> +J. Op. Soc. Am., 9, 335, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_312" href="#FNanchor_312" class="label">[312]</a> +Catalan, Phil. Trans., 223A, 127, 1922.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_313" href="#FNanchor_313" class="label">[313]</a> +Chapter VIII, <a href="#Page_124">p. 124</a>.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_314" href="#FNanchor_314" class="label">[314]</a> +H. C. 238, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_315" href="#FNanchor_315" class="label">[315]</a> +J. Op. Soc. Am., 9, 355, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_316" href="#FNanchor_316" class="label">[316]</a> +Phil. Trans., 223A, 127, 1922.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_317" href="#FNanchor_317" class="label">[317]</a> +Walters, J. Op. Soc. Am., 8, 245, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_318" href="#FNanchor_318" class="label">[318]</a> +Chapter VIII, <a href="#Page_125">p. 125</a>.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_319" href="#FNanchor_319" class="label">[319]</a> +<i>Ibid.</i></p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_320" href="#FNanchor_320" class="label">[320]</a> +Pub. Dom. Ap. Obs., 3, 7, 1925.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_321" href="#FNanchor_321" class="label">[321]</a> +H. C. 258, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_322" href="#FNanchor_322" class="label">[322]</a> +Chapter VIII, <a href="#Page_126">p. 126</a>.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_323" href="#FNanchor_323" class="label">[323]</a> +Mt. W. Contr., in press.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_324" href="#FNanchor_324" class="label">[324]</a> +Walters, J. Wash. Ac. Sci., 14, 408, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_325" href="#FNanchor_325" class="label">[325]</a> +Russell, Ap. J., 55, 119, 1922.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_326" href="#FNanchor_326" class="label">[326]</a> +Menzel, H. C. 258, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_327" href="#FNanchor_327" class="label">[327]</a> +Ap. J., 9, 214, 1899.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_328" href="#FNanchor_328" class="label">[328]</a> +Russell, Ap. J., 55, 119, 1922.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_329" href="#FNanchor_329" class="label">[329]</a> +Menzel, H. C. 258, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_330" href="#FNanchor_330" class="label">[330]</a> +Chapter VIII, <a href="#Page_126">p. 126</a>.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_331" href="#FNanchor_331" class="label">[331]</a> +Chapter XII, <a href="#Page_169">p. 169</a>.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_332" href="#FNanchor_332" class="label">[332]</a> +Pub. Dom. Ap. Obs., 2, 287, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_333" href="#FNanchor_333" class="label">[333]</a> +Meggers, J. Wash. Ac. Sci., 14, 419, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_334" href="#FNanchor_334" class="label">[334]</a> +<i>Ibid.</i></p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_335" href="#FNanchor_335" class="label">[335]</a> +de Gramont, C. R., 171, 1106, 1920.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_336" href="#FNanchor_336" class="label">[336]</a> +Merrill, Pub. A. S. P., 33, 206, 1921.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_337" href="#FNanchor_337" class="label">[337]</a> +King, Pub. A. S. P., 36, 140, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_338" href="#FNanchor_338" class="label">[338]</a> +Kiess, Bur. Stan. Sci. Pap. 474, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_339" href="#FNanchor_339" class="label">[339]</a> +Catalan, An. Soc. Espan. Fis. y Quim., 21, 84 and 213, 1923.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_340" href="#FNanchor_340" class="label">[340]</a> +Russell, Science, 39, 791, 1914.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_341" href="#FNanchor_341" class="label">[341]</a> +M. N. R. A. S., 77, 487, 1907.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_342" href="#FNanchor_342" class="label">[342]</a> +Russell, Ap. J., 55, 119, 1922.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_343" href="#FNanchor_343" class="label">[343]</a> +Saha, Phil. Mag., 40, 472, 1920.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_344" href="#FNanchor_344" class="label">[344]</a> +H. H. Plaskett, Pub. Dom. Ap. Obs., 1, 325, 1922.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_345" href="#FNanchor_345" class="label">[345]</a> +M. C. Johnson, M. N. R. A. S., 84, 516, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_346" href="#FNanchor_346" class="label">[346]</a> +Menzel, H. C. 258, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_347" href="#FNanchor_347" class="label">[347]</a> +Kiess, Pub. Obs. Mich., 3, 106, 1923.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_348" href="#FNanchor_348" class="label">[348]</a> +Mitchell, Ap. J., 38, 407, 1913.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_349" href="#FNanchor_349" class="label">[349]</a> +Gousmid, Naturwiss., 41, 851, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_350" href="#FNanchor_350" class="label">[350]</a> +A. N., 191, 393, 1912.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_351" href="#FNanchor_351" class="label">[351]</a> +A. N., 192, 82, 1912.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_352" href="#FNanchor_352" class="label">[352]</a> +A. N., 192, 266, 1912.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_353" href="#FNanchor_353" class="label">[353]</a> +Chapter I, <a href="#Page_5">p. 5</a>.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_354" href="#FNanchor_354" class="label">[354]</a> +Abbot, The Sun, 92, 1911.</p> + +</div> +</div> + +<hr class="chap x-ebookmaker-drop"> + +<div class="chapter"> +<p><span class="pagenum" id="Page_89">[Pg 89]</span></p> + +<h2 class="nobreak" id="PART_II">PART II<br> +THEORY OF THERMAL IONIZATION</h2> +</div> + +<p><span class="pagenum" id="Page_90">[Pg 90]</span></p> + +<hr class="chap x-ebookmaker-drop"> + +<div class="chapter"> +<p><span class="pagenum" id="Page_91">[Pg 91]</span></p> + +<h2 class="nobreak" id="CHAPTER_VI">CHAPTER VI<br> +THE HIGH-TEMPERATURE ABSORPTION SPECTRUM OF A GAS</h2> +</div> + + +<p class="nind"> +IT is certain that the conditions of which we see the integrated result +in the stellar spectrum are exceedingly complicated. Unfortunately, +the superficial portion of the star about which direct observational +evidence can be obtained is far less tractable to theory than is the +interior. Progress is only made possible by treating at the outset +a simplified case, by aiming merely at approximate results, and in +particular by limiting the preliminary discussion to the factors which +are numerically the most effective. As an introduction to the theory of +thermal ionization, the present chapter aims at the reconstruction and +interpretation of a stellar spectrum by applying known physical laws +under very simple conditions.</p> + +<p>The stellar reversing layer may be represented by an optically thin +layer of gas, at a pressure of the order of one ten thousandth of +an atmosphere; it lies between the observer and a photosphere which +radiates as a black body. The observer receives the radiation from +both reversing layer and photosphere, which are regarded, in the +present descriptive section, as independent. A more complete treatment +would take account of the temperature and pressure gradients in the +atmosphere of the star, the flux of energy, and the consequent intimate +connection between reversing layer and photosphere. Actually they +grade imperceptibly one into the other. The photosphere is that level +in the atmosphere at which the general opacity cuts off the direct +light from the interior;<a id="FNanchor_355" href="#Footnote_355" class="fnanchor">[355]</a> in the case discussed the reversing +layer is considered to be optically so thin that the general opacity +is negligible. The <i>selective</i> opacity, depending on the natural +absorption frequencies of the atoms present in the gas, gives rise +<span class="pagenum" id="Page_92">[Pg 92]</span> to +the line absorption spectrum which we are about to consider; the region +of sensible <i>general</i> opacity, represented by the photosphere, +gives rise to a continuous spectrum corresponding to the continuous +background in the star.</p> + + +<p class="nindc space-above2"> +THE ABSORPTION OF RADIATION</p> + + +<p>The light passing through the layer of gas is absorbed, in terms of +atomic theory, in the shifting of an electron from one energy level +in an atom to some higher level, losing in the process energy of the +definite frequency which is associated with that particular atom and +energy transfer. The energy levels and possible electron transfers +for the hydrogen atom are reproduced in <a href="#i002">Figures 2</a> and <a href="#i003">3</a>. In <a href="#i003">Figure 3</a> the horizontal lines represent the stationary states which can be +assumed by the electron, and the arrows denote possible jumps from +one stationary state to another. In <a href="#i002">Figure 2</a> the electron orbits +corresponding to some of the simpler corresponding transitions for +the hydrogen atom are represented. Arrows denote transfers from one +orbit to another. The designation of the line corresponding to each +transfer is appended to the appropriate arrow. It is evident that the +occurrence of a given jump requires that there shall be an electron in +the stationary state from which the jump originates.</p> + +<p>The <i>ultimate lines</i><a id="FNanchor_356" href="#Footnote_356" class="fnanchor">[356]</a><a id="FNanchor_357" href="#Footnote_357" class="fnanchor">[357]</a> are those which arise from the +lowest energy level, and are therefore those most readily absorbed by +the normal (undisturbed) atom. In the hydrogen spectrum these comprise +the Lyman series,<a id="FNanchor_358" href="#Footnote_358" class="fnanchor">[358]</a> with the first member at 1215.68. The Balmer and +Paschen series are both <i>subordinate</i> series, requiring an initial +lifting of the electron from the lowest energy level into a two and +three (total) quantum orbit, respectively. The absorption of the Lyman +line Ly \(\alpha\) is necessary to a hydrogen atom before it is in a +fit condition to absorb any Balmer line, and for the absorption of a +Paschen line, an initial absorption of Ly \(\beta\) or H \(\alpha\) is +required.</p> + +<p><span class="pagenum" id="Page_93">[Pg 93]</span></p> + +<p>It appears plausible to assume, at least for low partial pressures, +that the amount of energy of any frequency that is lost by black-body +radiation in passing through the absorbing layer will vary jointly with +the supply of energy and the number of atoms which are in a suitable +state to absorb that particular frequency. One of the problems that +arise is therefore that of determining what fraction of the whole +number of atoms of a given kind will be able to absorb. It is to this +problem that ionization theory is able to offer a solution.</p> + +<p>By choosing the much simplified case of very low pressure and small +concentration, the effects of ionization by collision<a id="FNanchor_359" href="#Footnote_359" class="fnanchor">[359]</a> and of +nuclear fields are probably eliminated. The remaining factor which may +influence the number of absorbing atoms is thermal ionization, and this +is actually the numerically important factor, as was first pointed out +by Saha.<a id="FNanchor_360" href="#Footnote_360" class="fnanchor">[360]</a> It is of interest to note that Saha’s original treatment +contemplated pressures of the order of one atmosphere. Under such +conditions the effects of collisions and of nuclear fields are +not negligible, and might well have invalidated the theory. Later +work has shown conclusively, however, that the pressures in the +reversing layer are probably not greater than +\(\displaystyle{10^{-4}\,\text{atmospheres}}\),<a id="FNanchor_361" href="#Footnote_361" class="fnanchor">[361]</a><a id="FNanchor_362" href="#Footnote_362" class="fnanchor">[362]</a> and +that thermal ionization is the predominant factor under these conditions.</p> + +<p><span class="pagenum" id="Page_94">[Pg 94]</span></p> + +<p>The absorbing layer is to be regarded as consisting of a mixture of +all chemical elements, without any assumption as to quantity, so long +as the partial pressure of each individual element is low. In other +words, no account is taken, at the present stage, of the relative +abundances of different kinds of atoms—the <i>total</i> effectiveness +of the corresponding elements as absorbers. The <i>changes</i> in the +absorption of the black body radiation by a given element with changing +temperature will be the same whatever the partial pressure, provided +it is low, and it is with these changes that the preliminary schematic +discussion is concerned.</p> + + +<p class="nindc space-above2"> +LOW TEMPERATURE CONDITIONS</p> + + +<p>At low temperatures all the elements will tend to be in their normal +atomic state, unless they are aggregated into molecules or compounds. +At temperatures of 2500°, which is about the lower limit encountered +in dealing with stellar spectra, there is evidence of the existence of +various oxides (CO, TiO₂, ZrO₂), of “cyanogen,” and of hydrocarbons, +but most of the other possible compounds appear either to be +dissociated or to be in very low concentration. Probably the normally +polyatomic gases such as oxygen, nitrogen, and sulphur, are to some +extent present in the molecular state. Even at atmospheric pressure all +the metals are vaporized at 2500° excepting tantalum and the platinum +metals, which boil at about 2800° under a pressure of 760 mm; at lower +pressures the temperature of vaporization is, of course, lower. The +metallic molecule appears normally to be monatomic, so that it will +give its line spectrum unless it is in combination. The fact that +silicon, the most refractory substance, excepting carbon, with which +we have to deal, gives its line spectrum in the coolest stars known, +indicates that all the elements may be considered to be gaseous in +stellar atmospheres.</p> + + +<p class="nindc space-above2"> +ULTIMATE LINES</p> + + +<p>The absorption spectrum given by the reversing layer when it is at a +low temperature will consist of the lines given most readily by the +atom in its normal state. The energy transfers which move an electron +from its normal orbit to another correspond to the “ultimate lines,” +and these lines will therefore be especially outstanding in the +spectra of the coolest atmospheres. They are of such importance, from +theoretical and from practical standpoints, that a list of them is +reproduced here. Successive columns of the table give the atomic number +and atom, the ionization potential, the wave-lengths of the ultimate +lines, and an indication of their observed occurrence in stellar +spectra. An asterisk denotes that the line has been observed, and a +dash indicates that it has not been recorded.</p> + +<p><span class="pagenum" id="Page_95">[Pg 95]</span></p> + +<p>It may be remarked that the ultimate lines of sodium, potassium, +lithium, rubidium, and caesium are in the visible region—a fact +which is utilized in the laboratory flame tests used in qualitative +analysis.<a id="FNanchor_363" href="#Footnote_363" class="fnanchor">[363]</a> The brilliancy of the flame colors obtained in the +Bunsen burner, at the temperature of about 1500°C., is a striking +elementary illustration of the readiness with which the atom in its +normal state will take up and re-emit the frequency corresponding to +the ultimate lines (second pair for K, Rb, Cs).</p> + +<h2><a id="TABLE_XVII">TABLE XVII</a></h2> + +<table class="autotable"> +<thead><tr> +<th class="tdc bb bt2 br" colspan="2">Atom </th> +<th class="tdc_ws1 bb bt2 br">Ionization<br> +Potential </th> +<th class="tdc bb bt2 br">Wave-lenght </th> +<th class="tdc_ws1 bb bt2"> Stellar<br> +Ocurrence</th> +</tr> +</thead> +<tbody><tr> +<td class="tdl">1</td> +<td class="tdl br">H</td> +<td class="tdc br">13.54</td> +<td class="tdr br">1215</td> +<td class="tdc">-</td> +</tr><tr> +<td class="tdl">2</td> +<td class="tdl br">He</td> +<td class="tdc br">24.47</td> +<td class="tdr br">584, 557</td> +<td class="tdc">-</td> +</tr><tr> +<td class="tdl">3</td> +<td class="tdl br">Li</td> +<td class="tdc br">5.37</td> +<td class="tdr br">6707</td> +<td class="tdc">*</td> +</tr><tr> +<td class="tdl">4</td> +<td class="tdl br">Be</td> +<td class="tdc br">?</td> +<td class="tdr br">2349</td> +<td class="tdc">-</td> +</tr><tr> +<td class="tdl">5</td> +<td class="tdl br">B</td> +<td class="tdc br">?</td> +<td class="tdr br">2498, 2497</td> +<td class="tdc">-</td> +</tr><tr> +<td class="tdl">6</td> +<td class="tdl br">C</td> +<td class="tdc br">?</td> +<td class="tdr br">2479</td> +<td class="tdc">-</td> +</tr><tr> +<td class="tdl">7</td> +<td class="tdl br">N</td> +<td class="tdc br">?</td> +<td class="tdr br">-</td> +<td class="tdc">-</td> +</tr><tr> +<td class="tdl">8</td> +<td class="tdl br">O</td> +<td class="tdc br">13.56</td> +<td class="tdr br">1306, 1304, 1302</td> +<td class="tdc">-</td> +</tr><tr> +<td class="tdl">9</td> +<td class="tdl br">F</td> +<td class="tdc br">?</td> +<td class="tdr br">-</td> +<td class="tdc">-</td> +</tr><tr> +<td class="tdl">10</td> +<td class="tdl br">Ne</td> +<td class="tdc br">16.7</td> +<td class="tdr br">-</td> +<td class="tdc">-</td> +</tr><tr> +<td class="tdl">11</td> +<td class="tdl br">Na</td> +<td class="tdc br">5.12</td> +<td class="tdr br">5896, 5890</td> +<td class="tdc">*</td> +</tr><tr> +<td class="tdl">12</td> +<td class="tdl br">Mg</td> +<td class="tdc br">7.61</td> +<td class="tdr br">2852</td> +<td class="tdc">-</td> +</tr><tr> +<td class="tdl">13</td> +<td class="tdl br">Al</td> +<td class="tdc br">5.96</td> +<td class="tdr br">3962, 3944</td> +<td class="tdc">-</td> +</tr><tr> +<td class="tdl">14</td> +<td class="tdl br">Si</td> +<td class="tdc br">?</td> +<td class="tdr br">2882</td> +<td class="tdc">-</td> +</tr><tr> +<td class="tdl">15</td> +<td class="tdl br">P</td> +<td class="tdc br">?</td> +<td class="tdr br">2553, 2536</td> +<td class="tdc">-</td> +</tr><tr> +<td class="tdl">16</td> +<td class="tdl br">S</td> +<td class="tdc br">10.31</td> +<td class="tdr br">1915, 1900</td> +<td class="tdc">-</td> +</tr><tr> +<td class="tdl">17</td> +<td class="tdl br">Cl</td> +<td class="tdc br">?</td> +<td class="tdr br">-</td> +<td class="tdc">-</td> +</tr><tr> +<td class="tdl">18</td> +<td class="tdl br">A</td> +<td class="tdc br">?</td> +<td class="tdr br">-</td> +<td class="tdc">-</td> +</tr><tr> +<td class="tdl">19</td> +<td class="tdl br">K</td> +<td class="tdc br">4.32</td> +<td class="tdr br">7699, 7665</td> +<td class="tdc">*</td> +</tr><tr> +<td class="tdl">20</td> +<td class="tdl br">Ca</td> +<td class="tdc br">6.09</td> +<td class="tdr br">4227</td> +<td class="tdc">*</td> +</tr><tr> +<td class="tdl">21</td> +<td class="tdl br">Sc</td> +<td class="tdc br">?</td> +<td class="tdr br">4247, 3652</td> +<td class="tdc">*</td> +</tr><tr> +<td class="tdl">22</td> +<td class="tdl br">Ti</td> +<td class="tdc br">6.5</td> +<td class="tdr br">5065, 5040, 5014</td> +<td class="tdc">*</td> +</tr><tr> +<td class="tdl">23</td> +<td class="tdl br">V</td> +<td class="tdc br">?</td> +<td class="tdr br">4331, 4333</td> +<td class="tdc">*</td> +</tr><tr> +<td class="tdl">24</td> +<td class="tdl br">Cr</td> +<td class="tdc br">6.75</td> +<td class="tdr br">4290, 4275, 5254</td> +<td class="tdc">*</td> +</tr><tr> +<td class="tdl">25</td> +<td class="tdl br">Mn</td> +<td class="tdc br">7.41</td> +<td class="tdr br">4034, 4033, 4031</td> +<td class="tdc">*</td> +</tr><tr> +<td class="tdl">26</td> +<td class="tdl br">Fe</td> +<td class="tdc br">?</td> +<td class="tdr br">2756, 2749</td> +<td class="tdc">-</td> +</tr><tr> +<td class="tdl">27</td> +<td class="tdl br">Co</td> +<td class="tdc br">?</td> +<td class="tdr br">3454, 3405</td> +<td class="tdc">*</td> +</tr><tr> +<td class="tdl">28</td> +<td class="tdl br">Ni</td> +<td class="tdc br">?</td> +<td class="tdr br">3415</td> +<td class="tdc">*</td> +</tr><tr> +<td class="tdl">29</td> +<td class="tdl br">Cu</td> +<td class="tdc br">7.69</td> +<td class="tdr br">3274, 3248</td> +<td class="tdc">* +<span class="pagenum" id="Page_96">[Pg 96]</span></td> +</tr><tr> +<td class="tdl">30</td> +<td class="tdl br">Zn</td> +<td class="tdc br">9.35</td> +<td class="tdr br">2139</td> +<td class="tdc">-</td> +</tr><tr> +<td class="tdl">31</td> +<td class="tdl br">Ga</td> +<td class="tdc br">5.97</td> +<td class="tdr br">4172, 4033</td> +<td class="tdc">*</td> +</tr><tr> +<td class="tdl">37</td> +<td class="tdl br">Rb</td> +<td class="tdc br">4.16</td> +<td class="tdr br">7948, 7800</td> +<td class="tdc">*</td> +</tr><tr> +<td class="tdl">38</td> +<td class="tdl br">Sr</td> +<td class="tdc br">5.67</td> +<td class="tdr br">4607</td> +<td class="tdc">*</td> +</tr><tr> +<td class="tdl">40</td> +<td class="tdl br">Zr</td> +<td class="tdc br">?</td> +<td class="tdr br">4496, 4392</td> +<td class="tdc">*</td> +</tr><tr> +<td class="tdl">42</td> +<td class="tdl br">Mo</td> +<td class="tdc br">?</td> +<td class="tdr br">3903, 3864, 3798</td> +<td class="tdc">*</td> +</tr><tr> +<td class="tdl">47</td> +<td class="tdl br">Ag</td> +<td class="tdc br">7.54</td> +<td class="tdr br">3383, 3281</td> +<td class="tdc">*</td> +</tr><tr> +<td class="tdl">48</td> +<td class="tdl br">Cd</td> +<td class="tdc br">8.95</td> +<td class="tdr br">2288</td> +<td class="tdc">-</td> +</tr><tr> +<td class="tdl">49</td> +<td class="tdl br">In</td> +<td class="tdc br">5.76</td> +<td class="tdr br">4511, 4102</td> +<td class="tdc">*</td> +</tr><tr> +<td class="tdl">50</td> +<td class="tdl br">Sn</td> +<td class="tdc br">?</td> +<td class="tdr br">3262</td> +<td class="tdc">?</td> +</tr><tr> +<td class="tdl">55</td> +<td class="tdl br">Cs</td> +<td class="tdc br">3.88</td> +<td class="tdr br">8943, 8581</td> +<td class="tdc">-</td> +</tr><tr> +<td class="tdl">56</td> +<td class="tdl br">Ba</td> +<td class="tdc br">5.19</td> +<td class="tdr br">7911</td> +<td class="tdc">-</td> +</tr><tr> +<td class="tdl">57</td> +<td class="tdl br">La</td> +<td class="tdc br">?</td> +<td class="tdr br">3949</td> +<td class="tdc">*</td> +</tr><tr> +<td class="tdl">79</td> +<td class="tdl br">Au</td> +<td class="tdc br">8.72</td> +<td class="tdr br">2676, 2428</td> +<td class="tdc">-</td> +</tr><tr> +<td class="tdl">80</td> +<td class="tdl br">Hg</td> +<td class="tdc br">10.39</td> +<td class="tdr br">2537, 1850</td> +<td class="tdc">-</td> +</tr><tr> +<td class="tdl">81</td> +<td class="tdl br">Tl</td> +<td class="tdc br">6.08</td> +<td class="tdr br">5350, 3775</td> +<td class="tdc">-</td> +</tr><tr> +<td class="tdl bb">82</td> +<td class="tdl bb br">Pb</td> +<td class="tdc bb br">7.38</td> +<td class="tdr bb br">4058, 3684</td> +<td class="tdc bb">*</td> +</tr> + </tbody> +</table> + +<p>It is possible to predict from the table which lines are likely to +appear in the spectra of the coolest stars. The ultimate lines of Al, +K, Ca, Sc, Ti, V, Cr, Mn, Co, Ni, Cu, Ga, Rb, Sr, Zr, Mo, Ag, In, Ba, +La, and Pb fall in the region ordinarily photographed, and Na can be +reached in the yellow. All these elements in the neutral state would +therefore be anticipated in the spectra of cooler stars, and they are +indeed found without exception. The ultimate lines of several elements +contained in the list lie in the far ultra-violet, and cannot be +detected in stellar spectra. The corresponding neutral elements will +therefore not be recorded unless they also give a strong subordinate +series in the photographic region. The elements C, O, S, and probably +N, all have ultimate lines in the ultra-violet, and possess no +subordinate series in the appropriate range of wave-length. Their +apparent absence in the neutral state from stellar spectra is therefore +fully explained. All of these elements appear in the hotter stars in +the once or twice ionized condition. The elements H, Mg, and Si have +strong subordinate series in the photographic region—the Balmer +<span class="pagenum" id="Page_97">[Pg 97]</span> +series, the “b” group, and the line<a id="FNanchor_364" href="#Footnote_364" class="fnanchor">[364]</a> at 3905, respectively. They +are accordingly represented in the cooler stars.</p> + +<p>The elements contained in the table and not yet discussed are Be, B, +Ne, A, F, and Cl. These elements have not been detected in stellar +spectra. In seeking an explanation of their apparent absence, it has +been suggested that a low relative abundance of the corresponding atoms +may be responsible. Arguments from terrestrial analogy must be applied +with caution, but there is reason to suspect that they may here have a +legitimate application.<a id="FNanchor_365" href="#Footnote_365" class="fnanchor">[365]</a> It may be suggested that boron, beryllium, +neon, and argon are present in the stars in quantities too small to be +detected. The halogens are unrepresented, but it is not possible to +draw useful inferences until their laboratory spectra are more fully +analyzed.</p> + + +<p class="nindc space-above2"> +IONIZATION</p> + + +<p>At the lowest temperatures, then, the ultimate lines will predominate. +As the temperature of the absorbing layer is raised, ionization—the +complete ejection of the electron from the atom, instead of a +displacement from one stationary state to another—will set in, and +the tracing of the resulting spectral changes is the salient feature +of the Saha theory. “Ionization can be effected in many ways. To expel +an electron against the attractive force of the remainder of the +molecule, work is required, and the necessary energy may be furnished +by X rays or \(\gamma\) rays, or by collision with other electrons.... +At high temperatures, when the conditions of maximum entropy demands an +appreciable amount of ionic dissociation, the requisite energy is drawn +from the environment.... The work required to ionize a single molecule, +when expressed as the number of volts through which an electron must +fall to acquire this energy, is the <i>ionization potential</i>; it may +be regarded as the latent heat of evaporation of the electron from the +molecule” (Milne).<a id="FNanchor_366" href="#Footnote_366" class="fnanchor">[366]</a></p> + +<p><span class="pagenum" id="Page_98">[Pg 98]</span></p> + +<p>The analogy between ionization and evaporation illustrates very well +the scope of the Saha theory, in which the process is treated as a +type of chemical dissociation. Corresponding to each temperature there +is a definite state of equilibrium, where the forward and backward +velocities of the ionization process are equal—in other words where +ionization and recombination are proceeding at the same rate. The +method of statistical mechanics has been applied to this problem by +Fowler and Milne.<a id="FNanchor_367" href="#Footnote_367" class="fnanchor">[367]</a> Here the analysis will not be reproduced, +but the formulae are required in order to illustrate the process of +ionization.</p> + +<p>The number of atoms which are unionized at any given temperature is +given by the expression +\[ +1 - x = \frac{b(T)}{b(T) + a T^{5/2}e^{- \chi_{1}/kT}} +\] +where \(x\) = number of atoms ionized.<br> +\(b(T)\) = the “partition function.”<br> +\(a = 0.332/P_e\), where \(P_e\) is the partial pressure of electrons.<br> +\(T\) = absolute temperature.<br> +\(k\) = Boltzmann’s constant, = \(1.37~\times~10^{-16}\).<br> +\(\chi_{1}\) = the ionization potential.</p> + +<p>This is the number of atoms which is effective in absorbing the +ultimate lines at that temperature. For low values of \(T\), the +number of unionized atoms falls off at first very slowly with rising +temperature, up to a point depending only on the ionization potential. +Beyond this temperature the number of neutral atoms falls off with +great rapidity. The diagram (<a href="#i005">Figure 5</a>) illustrates the fall in the +number of neutral atoms, and the consequent decay in strength of the +ultimate lines. So steep is the gradient of \(1 - x\) at the higher +temperatures that the quantity is best plotted logarithmically. The +ultimate lines will persist, with almost undiminished intensity, up to +the temperature at which the gradient of \(1 - x\) begins to increase. +<span class="pagenum" id="Page_99">[Pg 99]</span> +This critical temperature increases with ionization potential, and +neutral atoms of high ionization potential should display very +persistent ultimate lines as the temperature rises.</p> + +<figure class="figcenter" id="i005"> +<img src="images/i005.jpg" width="1510" height="2000" alt="i005"> +<figcaption class="caption"> + +<p>Figure 5</p> + +<p>Ultimate lines of neutral atoms. Ordinates are logarithms of computed +fractional concentrations; abscissae are temperatures in thousands of +degrees. The curves show the decrease in the number of neutral atoms, +with rising temperature, and the consequent decay in strength of the +ultimate lines, for the atoms indicated on the right margin.</p></figcaption> +</figure> + +<p>As ionization becomes more and more complete, the intensity of the +ultimate lines falls off until so small a number of neutral atoms +remains that their lines cease to appear in the absorption spectrum.</p> + + +<p class="nindc space-above2"> +SUBORDINATE LINES</p> + + +<p>The neutral atom gives rise to other lines besides the ultimate +lines, but these require the transfer of an electron from some +stationary state, not the normal one, to another stationary state. +The atom must receive a definite quantity of energy, equal to the +excitation potential of the initial stationary state, in order to +be in a condition to absorb a line of a subordinate +<span class="pagenum" id="Page_100">[Pg 100]</span> series which +originates from that state. If there is an appreciable energy supply, +a certain fraction of the neutral atoms present will have received +this excitation energy, which is of course smaller than the ionization +potential, and these atoms will be in a position to absorb the +subordinate series.</p> + +<figure class="figcenter" id="i006"> +<img src="images/i006.jpg" width="1597" height="2000" alt="i006"> +<figcaption class="caption"> + +<p>Figure 6</p> + +<p>Production of the maximum of an absorption line. Ordinates are +logarithms of computed fractional concentrations; abscissae are +temperatures in thousands of degrees. The curves reproduced are those +for the Mg + line at 4481. The upper broken curve represents the +fraction of magnesium atoms that is singly ionized at the corresponding +temperature; the lower broken curve represents the fraction of the Mg + +atoms present that is in a suitable state for the absorption of 4481. +The full line represents the sum of the ordinates of the dotted curves, +and gives the fraction of the total number of magnesium atoms that +is able to absorb 4481 at the various temperatures indicated by the +abscissae.</p></figcaption> +</figure> + +<p>The fraction, \(f_r\), of the total number of neutral atoms which have +<span class="pagenum" id="Page_101">[Pg 101]</span> +become able to absorb the lines associated with a definite excitation +potential is given by Fowler and Milne as +\[ +f_r = \frac{q_r e^{-(\chi_1 - \chi_1^{{}(r)})/kT}}{b(T)} +\] +where (\(\chi_1 - \chi_1^{(r)}\)) = excitation potential. The quantity +\(f_r\) increases with the temperature, approaching the value unity +asymptotically.</p> + +<p>The total number of atoms active in absorbing a subordinate series +at any temperature is evidently the product of the number of +<i>neutral</i> atoms and the quantity \(f_r\). The curves for these +two quantities are plotted logarithmically in <a href="#i006">Figure 6</a>, the magnesium +line 4481 being used as an illustration. The total number of absorbing +atoms may be obtained by adding the ordinates. It will be seen that the +number of such atoms increases, passes through a maximum and decreases +again, as the temperature is raised. The maximum for a subordinate +line of the neutral atom may occur, as in the case of helium, when +ionization is far advanced.</p> + +<p>In the special case where \(\chi_1 - \chi_1^{(r)} = 0\), the second +curve, which represents the growth of the fraction \(f_r\), becomes +a straight line parallel to the temperature axis, and the first, or +ionization, curve, approaches the zero ordinate asymptotically at low +temperatures. The ordinate of the curve representing \(f_r\) is zero, +and the resultant sum gives a curve identical with the curve for the +ultimate lines. Ultimate lines thus appear as the special case of +subordinate lines for which the excitation potential is zero. This fits +exactly with the definition of ultimate lines as the lines naturally +absorbed by the cold vapor—no initial excitation is required to bring +the atoms into a state in which they can absorb.</p> + + +<p class="nindc space-above2"> +LINES OF IONIZED ATOMS</p> + + +<p><span class="pagenum" id="Page_102">[Pg 102]</span></p> + +<p>As soon as ionization sets in, the absorbing layer begins to +contain a new kind of atom, derived from the neutral atoms by +the complete ejection of one electron. These ionized atoms will +absorb their own spectrum, which differs completely from that +of the corresponding neutral atom; and the degree of absorption +will again depend on the number of such ionized atoms present +in the reversing layer.</p> + +<p>The ionized atom has in general a spectrum corresponding +exactly to that of the neutral atom preceding it in the periodic +table, but with a different Rydberg constant.<a id="FNanchor_368" href="#Footnote_368" class="fnanchor">[368]</a><a id="FNanchor_369" href="#Footnote_369" class="fnanchor">[369]</a> Two types of +lines arise, as before—ultimate and subordinate lines. For +the number of atoms which can absorb the ultimate lines of the +enhanced spectrum, the formula reduces to +\[ +n_r = \frac{q_r e^{-(\chi_1 - \chi_1^{{}(r)})/kT}}{b(T) + \frac{P_e}{0.332 \sigma}T^{5/2}e^{-(\chi_1/kT)} ++ \frac{0.332 \sigma'}{P_e}T^{-5/2}e^{(\chi_2/kT)}} +\] +Account is here taken of the residual neutral atoms by the +middle term of the denominator, which is very small, and is +only of sensible magnitude for the ultimate lines, when the +numerator is equal to unity.</p> + +<figure class="figcenter" id="i007"> +<img src="images/i007.jpg" width="2000" height="1574" alt="i007"> +<figcaption class="caption"> + +<p>Figure 7</p> + +<p>Maximum of the ultimate line of an ionized atom. Ordinates are +logarithms of computed fractional concentrations; abscissae are +temperatures in thousands of degrees. The curve is drawn for +the line 4554 of Ba+, on the assumption that \(P_e\) is +\(\displaystyle{1.3~\times 10^{-4}~\text{atmospheres}}\).</p></figcaption> +</figure> + +<p>The following curve shows the number of absorbing atoms. The flatness +of the maximum is especially to be noted, suggesting that the ultimate +lines of the ionized atom, like the ultimate lines of the neutral +<span class="pagenum" id="Page_103">[Pg 103]</span> +atom, will be very persistent. The \(H\) and \(K\) lines of Ca+, and +the corresponding lines 4077 and 4215 of Sr+, and 4555 of Ba+, would +thus be expected to show over a considerable range in temperature and +spectrum, and this is actually found to be the case.</p> + +<p>The subordinate lines behave substantially as do the subordinate +lines of a neutral atom, rising to a maximum at a temperature which +depends chiefly on the ionization potential. It is assumed in deriving +the corresponding equations that in practice the number of surviving +neutral atoms will be too small to affect the concentration of ionized +atoms giving the subordinate lines. This assumption may be shown to be +justified at maximum intensity of the absorption line, though possibly +the neutral atoms are not always negligible at the first appearance of +the ionized lines of a very abundant atom.</p> + + +<p class="nindc space-above2"> +SUMMARY</p> + + +<p>The general results of raising the temperature of the absorbing layer +have now been traced. Although a greatly simplified case has been +considered, the observed changes in the stellar spectral sequence have +been very satisfactorily predicted.</p> + +<p>At low temperatures the lines of neutral atoms are strong, in +particular the ultimate lines, such as 3930 of Fe, 3999 of Ti, 4254 +of Cr, and 4033 of Mn, which are at maximum strength, and decrease at +first slowly, then rapidly in the hotter stars. The subordinate lines +of neutral atoms, 4455 of Ca and 4352 of Fe, for example, attain a +maximum, and then fall off with rising temperature. For many of the +metallic lines for which no maximum is recorded, like those of the +subordinate series of Na, the theoretical maximum is at a temperature +equal to that of the coolest stars examined. Atoms with ionization +potential less than 5 volts will in general give maxima below 3000°.</p> + +<p>As the temperature increases, the lines of ionized atoms begin to +appear, the ultimate lines rising very quickly in intensity, and +persisting almost at maximum over several spectral classes. Later in +the sequence the subordinate series for ionized atoms +<span class="pagenum" id="Page_104">[Pg 104]</span> appear, rise to +a sharper maximum, and fade more rapidly. The 4481 line of Mg+, the +4267 line of C+, and the 4128 line of Si+, show this effect well.</p> + +<p>As the fall of intensity of the lines of neutral atoms after maximum +is the result of the progress of ionization, it would be expected that +the lines of the ionized atom would appear while those of the neutral +atom were still quite strong, and that the one series would rise in +strength as the other decreased. The lines of the neutral atom may +persist over a large part of the range of the ionized lines. This is +the case with the 4227 line of Ca, which persists until Class \(A_0\), +while the \(H\) and \(K\) lines of Ca+ have been visible throughout +the whole spectral sequence, and have been decreasing in intensity +from \(K_0\) onwards, owing chiefly to the rise of second ionization +and the consequent formation of Ca++, which gives a spectrum in the +ultra-violet and is therefore not detected in the stars.</p> + +<p>As the temperature is further raised, the second and third ionizations +set in, and presumably follow the same procedure as has been outlined +for less ionized atoms. The lines of N++, C++, Si++, and Si+++ will +serve as examples. The lines of the doubly ionized atoms of the metals +are in general in the ultra-violet portion of the spectrum, and the +corresponding elements do not therefore appear in the hotter stars, +where they would otherwise be anticipated.</p> + +<p>Qualitatively the prediction of the theory of ionization is fully +satisfied. The quantitative discussion involves more rigorous +treatment, and is reserved for a later chapter.</p> + + +<div class="footnotes"><h3>FOOTNOTES:</h3> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_355" href="#FNanchor_355" class="label">[355]</a> +Stewart, Phys. Rev., 22, 324, 1923.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_356" href="#FNanchor_356" class="label">[356]</a> +De Gramont, C. R., 171, 1106, 1920.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_357" href="#FNanchor_357" class="label">[357]</a> +Russell, Pop. Ast., 32, 620, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_358" href="#FNanchor_358" class="label">[358]</a> +A. Fowler, Report on Series in Line Spectra, 1922.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_359" href="#FNanchor_359" class="label">[359]</a> +R. H. Fowler, Phil. Mag., 47, 257, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_360" href="#FNanchor_360" class="label">[360]</a> +Proc. Roy. Soc., 99A, 135, 1921.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_361" href="#FNanchor_361" class="label">[361]</a> +M. N. R. A. S., 83, 403, 1923; <i>ibid.</i>, 84, 499, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_362" href="#FNanchor_362" class="label">[362]</a> +Russell and Stewart, Ap. J., 59, 197, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_363" href="#FNanchor_363" class="label">[363]</a> +Eder and Valenta, Atlas Typischer Spektren, 10, 1911.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_364" href="#FNanchor_364" class="label">[364]</a> +See Chapter V, <a href="#Page_69">p. 69</a>. A. Fowler, Bakerian Lecture, 1924, +designates this an ultimate line.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_365" href="#FNanchor_365" class="label">[365]</a> +See Chapter XIII, <a href="#Page_185">p. 185</a>.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_366" href="#FNanchor_366" class="label">[366]</a> +Milne, Observatory, 44, 264, 1921.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_367" href="#FNanchor_367" class="label">[367]</a> +M. N. R. A. S., 83, 403, 1923; 84, 499, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_368" href="#FNanchor_368" class="label">[368]</a> +Sommerfeld, Atombau und Spektrallinien, 457, 1922.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_369" href="#FNanchor_369" class="label">[369]</a> +Meggers, Kiess, and Walters, Journ. Op. Soc. Am., 9, +355, 1924.</p> + +</div> +</div> + + +<hr class="chap x-ebookmaker-drop"> + +<div class="chapter"> +<p><span class="pagenum" id="Page_105">[Pg 105]</span></p> + +<h2 class="nobreak" id="CHAPTER_VII">CHAPTER VII<br> +CRITICAL DISCUSSION OF IONIZATION THEORY</h2> +</div> + + +<p class="nind"> +THE theory of thermal ionization, of which the preceding chapter +contains an illustrative discussion, may be treated from two points of +view—the sufficiency of the analytical treatment, and the nature of +the underlying physical assumptions. Actually the two questions are +merely two different ways of regarding the validity of the theory, +but they divide the discussion conveniently into a section dealing +with the analytical treatment and a section dealing with the physical +assumptions.</p> + +<p>The original treatment by Saha<a id="FNanchor_370" href="#Footnote_370" class="fnanchor">[370]</a> was based on the Law of Mass +Action, and the application to stellar atmospheres raised questions of +a physical rather than of an analytical nature. These questions are +fundamental not only to the Saha treatment, but also to the more recent +development of the theory, and they will be discussed in the second +half of the present chapter. The first half will be devoted to the +analytical formulae.</p> + + +<p class="nindc space-above2"> +MARGINAL APPEARANCE AND MAXIMUM</p> + + +<p>Saha’s discussion was based on the observation of “marginal +appearance”—the spectral class at which a particular absorption +line is at the limit of visibility. The use of this quantity as a +criterion for the temperature scale has certain practical drawbacks. +Marginal appearance depends directly on relative abundance, since a +more abundant element will give visible lines at a lower “fractional +concentration,” that is to say, when a smaller fraction of the element +is contributing to the lines in question. Further, in estimating the +intensities of lines in stellar spectra, difficulty is experienced when +the lines are faint, and the spectral class at which they are first +or last seen depends on their width and definition, the intensity +<span class="pagenum" id="Page_106">[Pg 106]</span> +of the continuous background, the presence of other lines, and the +dispersion used. All of these factors are subject to variation, and +in particular the intensity distribution in the continuous background +changes with the temperature. The statistical theory of Fowler and +Milne has, therefore, a great advantage in that it leads to an estimate +of the temperature at which a given line attains maximum. A maximum, +unlike a marginal appearance, can be determined without ambiguity from +homogeneous material, whatever the dispersion. In the cooler stars +the estimates may be made difficult by blending, but the uncertainty +can generally be removed by examining the maxima of several related +lines. Of the observational factors enumerated above as affecting the +estimation of marginal appearance, the changing intensity distribution +of the continuous background with the temperature is the only one that +may prove serious for the method of maxima.</p> + + +<p class="nindc space-above2"> +THEORETICAL FORMULAE</p> + + +<p>The theory developed by Fowler and Milne has been exhaustively +discussed by these authors in several papers, and it appears +unnecessary to reproduce the analysis in detail. The ionization and +excitation curves have been treated diagrammatically in the previous +chapter. The detailed formulae follow.</p> + +<p>“If \(\chi_{1}\) is the ionization potential of the atom, +\(\chi_1^{(r)}\) the (negative) energy of a given excited state, then +for a given partial electron pressure \(P_e\) of free electrons, the +temperature \(T\) of maximum concentration of atoms in the given +excited state +\(\chi_1^{(r)}\) is given by<a id="FNanchor_371" href="#Footnote_371" class="fnanchor">[371]</a> +\[ +P_{e}= \frac{\chi_{1}^{(r)} + \tfrac{5}{2} kT}{\chi_1 - \chi_{1}^{(r)}} +\cdot \frac{(2\pi m)^{3/2}(kT)^{5/2}\sigma_{1}}{h^{3}b_{1}(T)} \cdot e^{- \chi _{1}/kT} +\] +\[ +\begin{array}{l} +m = \text{mass of electron}.\\ +k = \text{Boltzmann’s constant}.\\ +h = \text{Planck’s constant}.\\ +\sigma = \text{symmetry number of the atom}\\ +\text{(number of spectroscopic valency electrons)}.\\ +b(T) = \text{the partition function}\\ +\quad\quad\,\,= q_{1} + q_1^{(2)}e^{-(\chi_{1} - \chi^{{}(2)})}/kT + e^{-(\chi_{1} - \chi^{{}(3)})}/kT + \dotsm\\ +q = \text{weight of corresponding stationary state}. +\end{array} +\]</p> + +<p><span class="pagenum" id="Page_107">[Pg 107]</span></p> + +<p>“The temperature at which the concentration of singly ionized atoms +reaches a maximum is given by<a id="FNanchor_372" href="#Footnote_372" class="fnanchor">[372]</a> +\[ +P_e = \left(\frac{\sigma_{1}\sigma_{2}}{{b_1(T)b_2(T)}}\right)^{1/2} +\left(\frac{\chi_{2} + \tfrac{5}{2} kt}{\chi_{1} + \tfrac{5}{2} kT}\right)^{1/2} +\frac{(2\pi m)^{3/2}(kT)^{5/2}}{h^{3}}e^{-\tfrac{1}{2}{(\chi_1 + \chi_2)/kT}} +\] +\[ +\begin{array}{l} +\chi_{2} = \text{second stage ionization potential}.\\ +\sigma_2~ \text{and}~ b_2(T)~ \text{refer to the singly ionization atom}. +\end{array} +\]</p> + +<p>The two formulae that have been quoted assume, in effect, that at +any stage of ionization the number of atoms, in stages other than +those whose constants appear in the formulae, is negligible. When +two ionizations occur in very close succession, this assumption no +longer holds, and the equations, as modified to embody the necessary +correction, are as follows.<a id="FNanchor_373" href="#Footnote_373" class="fnanchor">[373]</a></p> + +<p>For the subordinate series of a neutral atom, +\[ +P_e = \frac{\chi_{1}^{(r)} + \tfrac{5}{2} kT}{\chi_1 - \chi_{1}^{(r)}} \cdot \frac{(2\pi m)^{3/2}(kT)^{5/2}\sigma_{1}}{b_{1}(T)h^{3}} +\cdot e^{- \chi _{1}/kT} ++ \frac{1}{P_e}\frac{{\chi_2 - \chi_{1}^{(r)}} + 5 kT}{{\chi_1 - \chi_{1}^{(r)}}} +\cdot +\frac{(2\pi m)^{3}(kT)^{5}\sigma_{1}\sigma_{2}}{b_{1}(T)b_{2}(T)h^{6}} +\times e^{-{(\chi_1 + \chi_2)/kT}} +\]</p> + +<p>“This equation must be used to calculate \(P_e\) whenever +the ionization potential of the stage in question is closely +<i>followed</i> by the ionization potential of the succeeding stage.”</p> + +<p>For the subordinate series of the ionized atom, +\[ +P_e = \frac{\chi_{2}^{(r)} + \tfrac{5}{2} kT}{\chi_2 - \chi_{2}^{(r)}} +\cdot \frac{(2\pi m)^{3/2}(kT)^{5/2}\sigma_{2}}{b_{2}(T)h^{3}} +- \frac{P_e^{2}(\chi_1 + \chi_2 - \chi_{2}^{(r)}) + \tfrac{5}{2} kT}{{\chi_2 - \chi_{2}^{(r)}}} +\cdot +\frac{b_1(T)h^{3}}{(2\pi m)^{3/2}(kT)^{5/2}\sigma_1}e^{\chi_1/kT} +\] +<span class="pagenum" id="Page_108">[Pg 108]</span> +This equation “must be used wherever the ionization potential of +the stage in question is closely <i>preceded</i> by the ionization +potential of the preceding stage. The corrections ... result in making +the maxima for the lines of the two stages occur farther apart in +the temperature scale. If we express the correction in the +form of a factor (\(1 + a\)) ... then \(a\) is of the order +\(e^{-(\chi_2 - \chi_1)/kT_{max}}\). Since \(kT_{max}\) varies +roughly as \(\chi_1\) or \(\chi_2\), we see that the importance of the +correction is determined by the closeness of \(\chi_1/\chi_2\) to 1.”</p> + +<p>The values of \(n_r\), the fractional concentration of the atom in +question, are obtained through the application of the ordinary methods +of statistical mechanics to the equilibrium between atoms and electrons +in the reversing layer. The values of \(P_e\) at the maximum are +obtained by differentiating the expression for \(n_r\) with respect to +\(T\), and equating to zero, since the maximum of absorption will occur +when \(n_r\) is at a maximum.</p> + +<p>The analytical treatment calls for no comment. Its basis has been fully +discussed by R. H. Fowler<a id="FNanchor_374" href="#Footnote_374" class="fnanchor">[374]</a> in a series of papers. The weights +(\(q\)) of the atomic states employed were based on the work of +Bohr<a id="FNanchor_375" href="#Footnote_375" class="fnanchor">[375]</a> on the relative values of the a priori probabilities of the +different stationary states for hydrogen. On this view, \(b(T) = 1\) +for all atoms excepting those of H and He+, for which it is equal to +2. The convergence of the series for \(b(T)\) was not established by +Fowler and Milne, but the authors regard the subsequent investigation +by Urey<a id="FNanchor_376" href="#Footnote_376" class="fnanchor">[376]</a> as justifying their assumption that “for physical reasons +one must suppose the series effectively cut off after a certain number +of terms. Usually the series then reduces (as regards its numerical +value) practically to its first term.”</p> + + +<p class="nindc space-above2"> +PHYSICAL CONSTANTS REQUIRED IN THE FORMULAE</p> + + +<p>The application of the equations will of course depend upon an accurate +knowledge of the constants involved. The quantities \(m\), \(k\), +\(h\), and \(q\) require no comment. The symmetry number \(\sigma_1\) +<span class="pagenum" id="Page_109">[Pg 109]</span> +of the neutral atom is in effect the number of <i>spectroscopic</i> +valency electrons given in Bohr’s table,<a id="FNanchor_377" href="#Footnote_377" class="fnanchor">[377]</a> for the atoms for which +it is known. In all the applications made by Fowler and Milne the +quantity was equated to 1 or 2, and it is very probable that this +number is not in any case exceeded. For carbon, where the chemical +valency is equal to 4, the value of \(\sigma_1\) is still 2, as has +been shown by Fowler’s analysis of the spectrum of ionized carbon.<a id="FNanchor_378" href="#Footnote_378" class="fnanchor">[378]</a> +The value of \(\sigma_1\) is not known for atoms in the long periods, +but in the present work it is assumed to be 1 and 2 for atoms with +arc spectra which show even and odd multiplicities, respectively. The +uncertainty in the value of \(\sigma_1\) introduces only a relatively +small error into the result, since \(P_e\) depends on the first power +of \(\sigma_1\), and in no case considered can \(\sigma_1\) exceed five.</p> + +<p>The most important factor involved in the theory is \(P_e\), +the partial pressure of electrons in the reversing layer. +By assuming \(P_e\) constant at about +\(\displaystyle{10^{-4}~ \text{atmospheres}}\), and treating +\(T\) as the unknown, a temperature scale which agrees substantially +with those derived from measurements of radiation may be deduced from +the observed positions of the maxima. The first discussion of the +data then available was made by Fowler and Milne in their original +paper.<a id="FNanchor_379" href="#Footnote_379" class="fnanchor">[379]</a> Subsequent investigations of the positions of maxima +have been published by Menzel<a id="FNanchor_380" href="#Footnote_380" class="fnanchor">[380]</a> and by the writer.<a id="FNanchor_381" href="#Footnote_381" class="fnanchor">[381]</a> These +observations, and the scale derived from them, will be discussed in the +two following chapters.</p> + +<p>The value of \(P_e\) has been recently shown by several kinds of +investigation to be at least as low as was assumed by Fowler and +Milne, so that their assumption that a uniform mean pressure can be +used, as a first approximation, in deriving a temperature scale from +their formula appears to be justified. Milne<a id="FNanchor_382" href="#Footnote_382" class="fnanchor">[382]</a> points out that “on +whatever specific assumptions” the theory rests, “the mean pressure for +a maximum of intensity in an absorption line is found to depend on the +absolute value of the absorption coefficient. In fact ... it is clear +<span class="pagenum" id="Page_110">[Pg 110]</span> +that the greater the absorbing power of the atoms in question, the more +opaque is the stellar atmosphere in the frequency concerned, and so +the greater the height and the smaller the pressure at which the line +originates.” That the absorption coefficient in the stellar atmosphere +is very high is suggested by the reorganization times (“lives”) of such +atoms as have been investigated,<a id="FNanchor_383" href="#Footnote_383" class="fnanchor">[383]</a> and Milne’s discussion of the +life of the excited calcium atom from astrophysical data lends weight +to the suggestion. A high absorption coefficient leads at once +to low pressures in the reversing layer, and theory has gone +far towards indicating that pressures of the order of +\(\displaystyle{10^{-4}~ \text{atmospheres}}\) are to be expected +on a priori grounds.<a id="FNanchor_384" href="#Footnote_384" class="fnanchor">[384]</a></p> + +<p>The observational evidence bearing on pressures in the reversing layer +will be found<a id="FNanchor_385" href="#Footnote_385" class="fnanchor">[385]</a> in <a href="#CHAPTER_III">Chapter III</a>. The case appears to be a strong +one, resting on evidence of many different kinds—notably pressure +shifts, line sharpness, and series limits. Russell and Stewart,<a id="FNanchor_386" href="#Footnote_386" class="fnanchor">[386]</a> +in their exhaustive discussion of the question, conclude that “all +lines of evidence agree with the conclusion that the total pressure of +the <i>photospheric gases</i> is less than 0.01 atmosphere, and that +the average pressure in the <i>reversing layer</i> is not greater than +0.0001 atmosphere.”</p> + +<p>The observational evidence gives the <i>total</i> pressure, but the +partial electron pressure will not differ greatly from this. Although +even in the hottest stars three ionizations is the greatest number +observed, most of the elements that constitute the stellar atmosphere +are appreciably ionized at temperatures greater than 4000°, so that the +partial electron pressure is at least half the total pressure.</p> + + +<p class="nindc space-above2"> +PHYSICAL ASSUMPTIONS</p> + + +<p>The method applied by Saha to stellar atmospheres was borrowed +from physical chemistry. The Law of Mass Action, and the theory of +ionization in solutions which is based upon it, have in general been +very well satisfied in dilute solution.<a id="FNanchor_387" href="#Footnote_387" class="fnanchor">[387]</a> The ionization considered +<span class="pagenum" id="Page_111">[Pg 111]</span> +by chemical theory is the separation of a <i>molecule</i> in solution +into charged radicals. The essential point is the acquisition of a +charge at dissociation, and this is the only feature that the chemical +ionization has in common with the thermal ionization, where the +<i>atom</i> is separated into a positively charged ion and an electron +which constitutes the negative charge.</p> + +<p>The step from the theory first formulated for solutions to the theory +of gaseous ionization is a long one, and its legitimacy has been +questioned.<a id="FNanchor_388" href="#Footnote_388" class="fnanchor">[388]</a> It appears, however, that the step is justified.<a id="FNanchor_389" href="#Footnote_389" class="fnanchor">[389]</a> +The stellar conditions are certainly simpler than those in a +solution, and if the requisite dilution obtains, the law may be +expected to hold with considerable closeness. Saha contemplated +pressures of the order of an atmosphere, and it may be shown that under +such conditions the volume concentration would be too great and the +theory would be invalid. At pressures of +\(\displaystyle{10^{-4}~\text{atmospheres}}\), however, the +effect of concentration is just becoming inappreciable, and the theory +probably holds with fair exactness.</p> + + +<p class="nindc space-above2"> +LABORATORY EVIDENCE BEARING ON THE THEORY</p> + + +<p>(a) <i>Ultimate Lines</i><a id="FNanchor_390" href="#Footnote_390" class="fnanchor">[390]</a>—The physical tests of the Saha theory +that have been made in the laboratory have all supported it strongly. +The fact that the ultimate lines of an atom are the lines normally +absorbed by the cold vapor has long been familiar. Indeed it is this +fact that is tacitly assumed in the identification of lines of zero +excitation potential in the laboratory with lines which are strongest +in the low-temperature furnace spectrum. De Gramont<a id="FNanchor_391" href="#Footnote_391" class="fnanchor">[391]</a> designated the +ultimate lines “raies de grande sensibilité” for the detection of small +quantities of a substance, because they are the last to disappear from +the flame spectrum when the quantity of the substance is decreased.</p> + +<p><span class="pagenum" id="Page_112">[Pg 112]</span></p> + +<p>(b) <i>Temperature Class.</i>—The effect, upon the absorption +spectrum of a substance, of raising the temperature has also long been +recognized as an increase in the strength of lines associated with the +higher excitation potentials. The use of A. S. King’s “temperature +class” in assigning series relations<a id="FNanchor_392" href="#Footnote_392" class="fnanchor">[392]</a> involves a tacit admission +of the validity of the theory of thermal ionization in predicting +the relative numbers of atoms able to absorb light corresponding to +different levels of energy.<a id="FNanchor_393" href="#Footnote_393" class="fnanchor">[393]</a></p> + +<p>(c) <i>Furnace Experiments.</i>—King’s explicit investigation<a id="FNanchor_394" href="#Footnote_394" class="fnanchor">[394]</a> +of the effects of thermal ionization in the furnace has contributed +valuable positive evidence for the theory. For example, the production +of the subordinate series of the neutral atoms of the alkali metals +by raising the temperature was an experimental proof of the principle +mentioned in the last paragraph; and the suppression of the enhanced +lines of calcium by the presence of an excess of free electrons, +derived from the concurrent ionization of potassium, with an ionization +potential 1.77 volts lower than that of calcium, and the similar +results obtained for strontium and barium, fulfill the predictions of +ionization theory in a striking fashion.</p> + +<p><span class="pagenum" id="Page_113">[Pg 113]</span></p> + +<p>(d) <i>Conductivities of Flames.</i>—The conductivity of a flame may +be used as a measure of the ionization that is taking place at the +temperature in question, and the available data on flame conductivities +have been discussed by Noyes and Wilson<a id="FNanchor_395" href="#Footnote_395" class="fnanchor">[395]</a> from the standpoint of +the theory of thermal ionization. The calculations based upon the +conductivities imparted to a flame by the different alkali metals, and +leading to an estimate of the ionization constant, were in satisfactory +agreement with the theoretical predictions of the ionization constant +from the known critical potentials. The theory of thermal ionization +is, therefore, strongly supported by all the laboratory investigations +which have so far been undertaken in testing it.</p> + + +<p class="nindc space-above2"> +SOLAR INTENSITIES AS A TEST OF IONIZATION THEORY</p> + + +<p>Before proceeding to discuss the stellar intensity curves, it is +proposed to review some of the solar evidence, which can be treated +as an observational test of the predictions of the theory relating to +the distribution of atoms among the possible atomic states at a given +temperature.</p> + +<p>In two papers, Russell<a id="FNanchor_396" href="#Footnote_396" class="fnanchor">[396]</a> has given a discussion of the solar +and sunspot spectra, showing that ionization theory offers a very +satisfactory interpretation of most of the observed phenomena. +Attention was called to the anomalous behavior of barium and +lithium,<a id="FNanchor_397" href="#Footnote_397" class="fnanchor">[397]</a> and it was suggested that the theory of thermal +ionization, while taking account of the temperature of the reversing +layer, omitted to consider the effect of the absorption of photospheric +radiation. This omission might cause a deviation such as is observed +for barium, but appears inadequate to account for the behavior of +lithium. In the case of lithium, low atomic weight, and a consequent +high velocity of thermal agitation, has been suggested as the cause of +the anomaly. The question of the absorption of photospheric radiation +has more recently been discussed by Saha,<a id="FNanchor_398" href="#Footnote_398" class="fnanchor">[398]</a> in the form of a +correction to his own ionization equations. It has been pointed out by +Woltjer<a id="FNanchor_399" href="#Footnote_399" class="fnanchor">[399]</a> that the correction introduced by Saha and Swe may also be +derived from considerations advanced by Einstein<a id="FNanchor_400" href="#Footnote_400" class="fnanchor">[400]</a> and Milne.<a id="FNanchor_401" href="#Footnote_401" class="fnanchor">[401]</a> +The correction can be evaluated, but appears in every case to be rather +small. The effect of the photospheric radiation is certainly one that +must be included in a satisfactory theory, but at present, observation +is probably not of sufficient accuracy to demand such a refinement.</p> + +<p>The work just quoted was qualitative. A more quantitative test of +ionization theory in the solar spectrum can also be made<a id="FNanchor_402" href="#Footnote_402" class="fnanchor">[402]</a> by +comparing the intensities of solar lines corresponding to different +excitation potentials, but belonging to the same atom. The +<span class="pagenum" id="Page_114">[Pg 114]</span> atoms which +give a large number of lines in the solar spectrum are those of the +first long period of the periodic table, and these, as is well known, +consist of multiplets, with components of very different intensities. +It appears to be legitimate to select the strongest line associated +with any energy level for the comparison; the strength of this line +probably represents fairly well the tendency of the atom to be in the +corresponding state.</p> + +<table class="autotable"> +<thead><tr> +<th class="tdc bb bt2 br">Atom</th> +<th class="tdc_ws1 bb bt2 br">Excitation<br> +Potential</th> +<th class="tdc bb bt2 br"> \(log~ n_r\) </th> +<th class="tdc bb bt2 br"> Intensity </th> +<th class="tdc bb bt2 br">Atom</th> +<th class="tdc_ws1 bb bt2 br">Excitation<br> +Potential</th> +<th class="tdc bb bt2 br"> \(log~ n_r\) </th> +<th class="tdc bb bt2"> Intensity </th> +</tr> +</thead> +<tbody><tr> +<td class="tdl br">Calcium</td> +<td class="tdc br">0.00</td> +<td class="tdc br">\(\bar{2}.67\)</td> +<td class="tdc br">20</td> +<td class="tdl br">Chromium</td> +<td class="tdc br">0.00</td> +<td class="tdc br">\(\bar{1}.20\)</td> +<td class="tdc">10</td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">1.88</td> +<td class="tdc br">\(\bar{4}.97\)</td> +<td class="tdc br">15</td> +<td class="tdl br"></td> +<td class="tdc br">0.94</td> +<td class="tdc br">\(\bar{2}.38\)</td> +<td class="tdc">5</td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">2.53</td> +<td class="tdc br">\(\bar{4}.40\)</td> +<td class="tdc br">8</td> +<td class="tdl br"></td> +<td class="tdc br">1.02</td> +<td class="tdc br">\(\bar{2}.31\)</td> +<td class="tdc">5</td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">2.70</td> +<td class="tdc br">\(\bar{4}.26\)</td> +<td class="tdc br">5</td> +<td class="tdl br"></td> +<td class="tdc br">2.89</td> +<td class="tdc br">\(\bar{4}.66\)</td> +<td class="tdc">2</td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">2.92</td> +<td class="tdc br">\(\bar{4}.07\)</td> +<td class="tdc br">4</td> +<td class="tdl br">Titanium</td> +<td class="tdc br">0.00</td> +<td class="tdc br">\(\bar{1}.89\)</td> +<td class="tdc">5</td> +</tr><tr> +<td class="tdl br">Iron</td> +<td class="tdc br">0.00</td> +<td class="tdc br">\(\bar{2}.66\)</td> +<td class="tdc br">40</td> +<td class="tdl br"></td> +<td class="tdc br">0.82</td> +<td class="tdc br">\(\bar{2}.14\)</td> +<td class="tdc">4</td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">0.94</td> +<td class="tdc br">\(\bar{3}.86\)</td> +<td class="tdc br">30</td> +<td class="tdl br"></td> +<td class="tdc br">0.90</td> +<td class="tdc br">\(\bar{2}.08\)</td> +<td class="tdc">3</td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">1.54</td> +<td class="tdc br">\(\bar{3}.31\)</td> +<td class="tdc br">30</td> +<td class="tdl br"></td> +<td class="tdc br">1.05</td> +<td class="tdc br">\(\bar{3}.95\)</td> +<td class="tdc">3</td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">2.19</td> +<td class="tdc br">\(\bar{4}.71\)</td> +<td class="tdc br">8</td> +<td class="tdl br"></td> +<td class="tdc br">1.44</td> +<td class="tdc br">\(\bar{3}.81\)</td> +<td class="tdc">3</td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">2.46</td> +<td class="tdc br">\(\bar{4}.45\)</td> +<td class="tdc br">10</td> +<td class="tdl br"></td> +<td class="tdc br">1.50</td> +<td class="tdc br">\(\bar{3}.54\)</td> +<td class="tdc">2</td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">2.84</td> +<td class="tdc br">\(\bar{4}.08\)</td> +<td class="tdc br">8</td> +<td class="tdl br"></td> +<td class="tdc br">1.87</td> +<td class="tdc br">\(\bar{3}.21\)</td> +<td class="tdc">1</td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">2.96</td> +<td class="tdc br">\(\bar{4}.02\)</td> +<td class="tdc br">7</td> +<td class="tdl br"></td> +<td class="tdc br">1.98</td> +<td class="tdc br">\(\bar{3}.21\)</td> +<td class="tdc">1</td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">3.25</td> +<td class="tdc br">\(\bar{5}.77\)</td> +<td class="tdc br">7</td> +<td class="tdl br"></td> +<td class="tdc br">2.08</td> +<td class="tdc br">\(\bar{3}.04\)</td> +<td class="tdc">0</td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">3.38</td> +<td class="tdc br">\(\bar{5}.66\)</td> +<td class="tdc br">6</td> +<td class="tdl br"></td> +<td class="tdc br">2.16</td> +<td class="tdc br">\(\bar{4}.95\)</td> +<td class="tdc">1</td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">3.64</td> +<td class="tdc br">\(\bar{5}.39\)</td> +<td class="tdc br">8</td> +<td class="tdl br"></td> +<td class="tdc br">2.24</td> +<td class="tdc br">\(\bar{4}.89\)</td> +<td class="tdc">2</td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4.13</td> +<td class="tdc br">\(\bar{6}.93\)</td> +<td class="tdc br">-</td> +<td class="tdl br"></td> +<td class="tdc br">2.26</td> +<td class="tdc br">\(\bar{4}.85\)</td> +<td class="tdc">0</td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4.23</td> +<td class="tdc br">\(\bar{6}.86\)</td> +<td class="tdc br">-</td> +<td class="tdl br"></td> +<td class="tdc br">2.28</td> +<td class="tdc br">\(\bar{4}.83\)</td> +<td class="tdc">0</td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4.35</td> +<td class="tdc br">\(\bar{6}.84\)</td> +<td class="tdc br">-</td> +<td class="tdl br"></td> +<td class="tdc br">2.33</td> +<td class="tdc br">\(\bar{4}.80\)</td> +<td class="tdc">0</td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4.40</td> +<td class="tdc br">\(\bar{6}.70\)</td> +<td class="tdc br">-</td> +<td class="tdl br"></td> +<td class="tdc br">2.39</td> +<td class="tdc br">\(\bar{4}.75\)</td> +<td class="tdc"><span class="tight">00</span></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdl br"></td> +<td class="tdc br">2.47</td> +<td class="tdc br">\(\bar{4}.67\)</td> +<td class="tdc">-</td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdl br"></td> +<td class="tdc br">2.56</td> +<td class="tdc br">\(\bar{4}.60\)</td> +<td class="tdc"><span class="tight">000</span></td> +</tr><tr> +<td class="tdl bb br"></td> +<td class="tdc bb br"></td> +<td class="tdc bb br"></td> +<td class="tdc bb br"></td> +<td class="tdl bb br"></td> +<td class="tdc bb br">2.67</td> +<td class="tdc bb br">\(\bar{4}.52\)</td> +<td class="tdc bb"><span class="tight">000</span></td> +</tr> + </tbody> +</table> + +<p>The atoms for which there are enough known lines of different +excitation energies in the solar spectrum are those of calcium, +chromium, titanium, and iron. The correlation between the excitation +potential associated with a given line and the intensity of the line +in the solar spectrum is illustrated by the preceding tabulation. +Successive columns give the atom, the excitation potential, the +<span class="pagenum" id="Page_115">[Pg 115]</span> +computed fractional concentration, expressed logarithmically, and the +observed intensity, taken from Rowland’s table.</p> + +<p>It will be seen that the correlation is very marked, and that it +appears to furnish good evidence that the theory of thermal ionization +predicts correctly the relative tendencies of the atoms to absorb the +different frequencies. The fractional concentrations are of course not +absolute values, as the number of atoms in a state of high excitation +is a definite fraction, not of the <i>whole</i> number of atoms, but +of the <i>number left over</i> from the lower excitations. Neither are +the intensities given by Rowland absolute, and therefore the comparison +appears sufficient to show the strong correlation between excitation +potential and solar intensity.</p> + + +<div class="footnotes"><h3>FOOTNOTES:</h3> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_370" href="#FNanchor_370" class="label">[370]</a> +Proc. Roy. Soc., 99A, 136, 1921.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_371" href="#FNanchor_371" class="label">[371]</a> +M. N. R. A. S., 83, 403, 1923; <i>ibid.</i>, 84, 499, +1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_372" href="#FNanchor_372" class="label">[372]</a> +M. N. R. A. S., 83, 403, 1923.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_373" href="#FNanchor_373" class="label">[373]</a> +M. N. R. A. S., 84, 499, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_374" href="#FNanchor_374" class="label">[374]</a> +R. H. Fowler, Phil. Mag., 45, 1, 1923.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_375" href="#FNanchor_375" class="label">[375]</a> +Bohr, Mem. Ac. Roy. Den., 4, 2, 76, 1922.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_376" href="#FNanchor_376" class="label">[376]</a> +Ap. J., 59, 1, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_377" href="#FNanchor_377" class="label">[377]</a> +Chapter I, <a href="#Page_9">p. 9</a>.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_378" href="#FNanchor_378" class="label">[378]</a> +Proc. Roy. Soc., 103A, 413, 1923.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_379" href="#FNanchor_379" class="label">[379]</a> +M. N. R. A. S., 83, 404, 1923.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_380" href="#FNanchor_380" class="label">[380]</a> +H. C. 258, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_381" href="#FNanchor_381" class="label">[381]</a> +H. C. 252, 256, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_382" href="#FNanchor_382" class="label">[382]</a> +Phil. Mag., 47, 209, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_383" href="#FNanchor_383" class="label">[383]</a> +Chapter I, <a href="#Page_21">p. 21</a>.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_384" href="#FNanchor_384" class="label">[384]</a> +Proc. Phys. Soc. Lond., 36, 94, 924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_385" href="#FNanchor_385" class="label">[385]</a> +<a href="#Page_45">P. 45</a>.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_386" href="#FNanchor_386" class="label">[386]</a> +Ap. J., 59, 197, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_387" href="#FNanchor_387" class="label">[387]</a> +See, for instance, H. J. H. Fenton, Outlines of +Chemistry, 128, 1918.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_388" href="#FNanchor_388" class="label">[388]</a> +Lindemann, quoted by Milne, Observatory, 44, 264, 1921.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_389" href="#FNanchor_389" class="label">[389]</a> +Milne, Observatory, 44, 264, 1921.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_390" href="#FNanchor_390" class="label">[390]</a> +Chapter VI, <a href="#Page_94">p. 94</a>.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_391" href="#FNanchor_391" class="label">[391]</a> +C. R., 171, 1106, 1920.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_392" href="#FNanchor_392" class="label">[392]</a> +Russell, Ap. J., in press.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_393" href="#FNanchor_393" class="label">[393]</a> +A. S. King, Mt. W. Contr. 247, 1922.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_394" href="#FNanchor_394" class="label">[394]</a> +A. S. King, Mt. W. Contr. 233, 1922.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_395" href="#FNanchor_395" class="label">[395]</a> +Ap. J., 57, 20, 1923.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_396" href="#FNanchor_396" class="label">[396]</a> +Mt. W. Contr. 225, 1922.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_397" href="#FNanchor_397" class="label">[397]</a> +Mt. W. Contr. 236, 1922.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_398" href="#FNanchor_398" class="label">[398]</a> +Saha and Swe, Nature, 115, 377, 1925.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_399" href="#FNanchor_399" class="label">[399]</a> +Nature, 115, 534, 1925.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_400" href="#FNanchor_400" class="label">[400]</a> +Phys. Zeit., 18, 121, 1917.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_401" href="#FNanchor_401" class="label">[401]</a> +Phil. Mag., 47, 209, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_402" href="#FNanchor_402" class="label">[402]</a> +Payne, Proc. N. Ac. Sci., 11, 197, 1925.</p> + +</div> +</div> + +<hr class="chap x-ebookmaker-drop"> + +<div class="chapter"> +<p><span class="pagenum" id="Page_116">[Pg 116]</span></p> + +<h2 class="nobreak" id="CHAPTER_VIII">CHAPTER VIII<br> +OBSERVATIONAL MATERIAL FOR THE TEST OF IONIZATION THEORY</h2> +</div> + + +<p class="nind"> +THE observational test of ionization theory involves a considerable +program of measurement, if the accuracy necessary for a quantitative +test is to be attained. The present chapter contains a synopsis of +new data obtained by the writer to supplement the material already +published in Harvard Circulars.<a id="FNanchor_403" href="#Footnote_403" class="fnanchor">[403]</a><a id="FNanchor_404" href="#Footnote_404" class="fnanchor">[404]</a> The data here presented +practically complete the available material for the strong lines of +known series relations in the region of the spectrum usually examined.</p> + + +<p class="nindc space-above2"> +LINE INTENSITY</p> + + +<p>The theory predicts the degree of absorption that will be produced +by each atom at a given temperature, and the related quantity that +is measured is the intensity of the corresponding Fraunhofer line +in the spectrum of the star. Spectrum lines are differentiated by +various qualities, such as width, darkness, and wings, and their +conspicuousness is governed by the intensity of the neighboring +continuous background. It is not easy to specify all these quantities +on an intensity scale that is one-dimensional, and the various ways in +which line intensities have been estimated represent different attempts +to choose and express a suitable scale.</p> + +<p>Many of the applications of so-called line-intensity, such as the +estimation of spectroscopic parallaxes, have involved ratios between +the strengths of various lines in the same spectrum. This method of +comparison avoids most of the difficulties caused by differences of +line character and continuous background, for the lines that are to +be compared are chosen because of their proximity and comparability. +<span class="pagenum" id="Page_117">[Pg 117]</span> +Harper and Young<a id="FNanchor_405" href="#Footnote_405" class="fnanchor">[405]</a> have standardized the method by comparing +spectrum line ratios with line ratios on an artificial scale.</p> + + +<p class="nindc space-above2"> +METHOD OF ESTIMATING INTENSITY</p> + + +<p>In a comparison of ionization theory with observation, some measure of +line-intensity is required which can be compared from class to class. +It seems probable that direct estimates of intensity, for spectra of +the same dispersion, density, and definition, will be comparable within +the limits of accuracy of the material.</p> + +<p>Two series of spectra were measured by the writer in order to obtain +material for the test of the theory of ionization. For the first +group standard lines in the spectrum of \(\alpha\) Cygni were used +for the formation of a direct intensity scale, and for the second +group, comprising the cooler stars, a strip of the solar spectrum was +similarly employed. An arbitrary scale was constructed by assigning a +series of intensities to well placed lines in the spectrum, and using +these as standards. A list of the lines used for the second group, the +assigned intensity, and the intensity as given in Rowland’s table, are +contained in the following table.</p> + +<table class="autotable"> +<thead><tr> +<th class="tdc_bot" rowspan="2">Line </th> +<th class="tdc_top" colspan="2">Intensity</th> +<th class="tdc"></th> +<th class="tdc_bot" rowspan="2">Line</th> +<th class="tdc_top" colspan="2">Intensity</th> +</tr> +<tr> +<th class="tdc">Assigned </th> +<th class="tdc">Rowland </th> +<th class="tdc"></th> +<th class="tdc">Assigned </th> +<th class="tdc">Rowland</th> +</tr> +</thead> +<tbody><tr> +<td class="tdl">4034</td> +<td class="tdc">6</td> +<td class="tdc">7</td> +<td class="tdr"></td> +<td class="tdl">4046</td> +<td class="tdc">10</td> +<td class="tdc">30</td> +</tr><tr> +<td class="tdl">4035</td> +<td class="tdc">5</td> +<td class="tdc">6</td> +<td class="tdr"></td> +<td class="tdl">3968</td> +<td class="tdc">13</td> +<td class="tdc">700</td> +</tr><tr> +<td class="tdl">4038</td> +<td class="tdc">4</td> +<td class="tdc">4</td> +<td class="tdr"></td> +<td class="tdl">3934</td> +<td class="tdc">15</td> +<td class="tdc">1000</td> +</tr><tr> +<td class="tdl">4064</td> +<td class="tdc">8</td> +<td class="tdc">20</td> +<td class="tdr"></td> +<td class="tdl"></td> +<td class="tdc"></td> +<td class="tdc"></td> + +</tr> + </tbody> +</table> + +<p><span class="pagenum" id="Page_118">[Pg 118]</span></p> + +<p>The estimates thus made might be defined as estimates of +width-intensity-contrast between the line and the continuous +background. On an ideal plate which was not burned out, such estimates +would give a measure of the total energy of the line relative to the +neighboring continuous spectrum. The accuracy attained by direct +estimates of this kind appears to be as great as the material warrants.</p> + + +<p class="nindc space-above2"> +ACCURACY OF THE ESTIMATES</p> + + +<p>It is not possible at present to evaluate the accuracy of these +estimates with the same precision as for other physical quantities, +but the consistency of the readings from comparable plates of the +same star will at least give a measure of the value of the estimates. +<a href="#TABLE_XVIII">Table XVIII</a> contains the measures on forty-three lines in the spectrum +of \(\beta\) Gruis, taken from six plates of the same dispersion, +and comparable quality, density, and definition. Successive columns +give the wave-length, the arithmetic mean intensity, and the standard +deviation \(\sigma\).</p> + +<h2><a id="TABLE_XVIII">TABLEXVIII</a></h2> + +<table class="autotable"> +<thead><tr> +<th class="tdc bb bt2">Line </th> +<th class="tdc bb bt2"> Int. </th> +<th class="tdc bb bt2 br">\(\sigma\) </th> +<th class="tdc bb bt2">Line </th> +<th class="tdc bb bt2"> Int. </th> +<th class="tdc bb bt2 br">\(\sigma\) </th> +<th class="tdc bb bt2">Line </th> +<th class="tdc bb bt2"> Int. </th> +<th class="tdc bb bt2 br">\(\sigma\) </th> +<th class="tdc bb bt2">Line </th> +<th class="tdc bb bt2"> Int. </th> +<th class="tdc bb bt2 br">\(\sigma\) </th> +</tr> +</thead> +<tbody><tr> +<td class="tdc">4215</td> +<td class="tdc">8.4</td> +<td class="tdc br">1.0</td> +<td class="tdc">4319</td> +<td class="tdc">4.8</td> +<td class="tdc br">0.8</td> +<td class="tdc">4376</td> +<td class="tdc">7.8</td> +<td class="tdc br">0.6</td> +<td class="tdc">4451</td> +<td class="tdc">4.5</td> +<td class="tdc br">1.5</td> +</tr><tr> +<td class="tdc">4227</td> +<td class="tdc">16.0</td> +<td class="tdc br">1.4</td> +<td class="tdc">4321</td> +<td class="tdc">4.0</td> +<td class="tdc br">0.0</td> +<td class="tdc">4379</td> +<td class="tdc">4.2</td> +<td class="tdc br">0.3</td> +<td class="tdc">4455</td> +<td class="tdc">5.0</td> +<td class="tdc br">1.0</td> +</tr><tr> +<td class="tdc">4247</td> +<td class="tdc">6.0</td> +<td class="tdc br">0.0</td> +<td class="tdc">4326</td> +<td class="tdc">10.4</td> +<td class="tdc br">0.5</td> +<td class="tdc">4383</td> +<td class="tdc">10.3</td> +<td class="tdc br">0.8</td> +<td class="tdc">4462</td> +<td class="tdc">6.0</td> +<td class="tdc br">0.8</td> +</tr><tr> +<td class="tdc">4250</td> +<td class="tdc">7.0</td> +<td class="tdc br">0.0</td> +<td class="tdc">4330</td> +<td class="tdc">4.6</td> +<td class="tdc br">0.8</td> +<td class="tdc">4395</td> +<td class="tdc">6.3</td> +<td class="tdc br">0.4</td> +<td class="tdc">4482</td> +<td class="tdc">7.7</td> +<td class="tdc br">0.7</td> +</tr><tr> +<td class="tdc">4254</td> +<td class="tdc">9.0</td> +<td class="tdc br">1.0</td> +<td class="tdc">4332</td> +<td class="tdc">3.6</td> +<td class="tdc br">0.5</td> +<td class="tdc">4398</td> +<td class="tdc">2.7</td> +<td class="tdc br">0.8</td> +<td class="tdc">4490</td> +<td class="tdc">7.3</td> +<td class="tdc br">0.4</td> +</tr><tr> +<td class="tdc">4260</td> +<td class="tdc">9.0</td> +<td class="tdc br">2.1</td> +<td class="tdc">4333</td> +<td class="tdc">4.0</td> +<td class="tdc br">0.0</td> +<td class="tdc">4402</td> +<td class="tdc">6.3</td> +<td class="tdc br">0.4</td> +<td class="tdc">4495</td> +<td class="tdc">7.5</td> +<td class="tdc br">0.4</td> +</tr><tr> +<td class="tdc">4272</td> +<td class="tdc">8.7</td> +<td class="tdc br">0.8</td> +<td class="tdc">4337</td> +<td class="tdc">8.7</td> +<td class="tdc br">0.8</td> +<td class="tdc">4405</td> +<td class="tdc">9.0</td> +<td class="tdc br">0.5</td> +<td class="tdc">4502</td> +<td class="tdc">6.0</td> +<td class="tdc br">0.0</td> +</tr><tr> +<td class="tdc">4275</td> +<td class="tdc">9.5</td> +<td class="tdc br">1.3</td> +<td class="tdc">4340</td> +<td class="tdc">9.5</td> +<td class="tdc br">1.1</td> +<td class="tdc">4409</td> +<td class="tdc">9.0</td> +<td class="tdc br">0.5</td> +<td class="tdc">4554</td> +<td class="tdc">5.3</td> +<td class="tdc br">0.4</td> +</tr><tr> +<td class="tdc">4283</td> +<td class="tdc">4.3</td> +<td class="tdc br">0.4</td> +<td class="tdc">4352</td> +<td class="tdc">9.2</td> +<td class="tdc br">1.1</td> +<td class="tdc">4415</td> +<td class="tdc">7.7</td> +<td class="tdc br">0.8</td> +<td class="tdc">4564</td> +<td class="tdc">5.8</td> +<td class="tdc br">0.7</td> +</tr><tr> +<td class="tdc">4290</td> +<td class="tdc">10.6</td> +<td class="tdc br">1.0</td> +<td class="tdc">4360</td> +<td class="tdc">6.8</td> +<td class="tdc br">1.0</td> +<td class="tdc">4435</td> +<td class="tdc">9.2</td> +<td class="tdc br">0.9</td> +<td class="tdc">4572</td> +<td class="tdc">6.0</td> +<td class="tdc br">1.0</td> +</tr><tr> +<td class="tdc bb">4315</td> +<td class="tdc bb">8.3</td> +<td class="tdc bb br">0.7</td> +<td class="tdc bb">4370</td> +<td class="tdc bb">6.8</td> +<td class="tdc bb br">0.6</td> +<td class="tdc bb">4444</td> +<td class="tdc bb">8.9</td> +<td class="tdc bb br">1.2</td> +<td class="tdc bb"></td> +<td class="tdc bb"></td> +<td class="tdc bb br"></td> +</tr> + </tbody> +</table> + + +<p>These measures are strictly representative of the material as a whole, +for the plates of \(\beta\) Gruis were measured at wide intervals in +the ordinary course of the work, and were selected for illustration +because there was a greater number of suitable plates of this star than +for any other.</p> + + +<p class="nindc space-above2"> +HOMOGENEITY OF MATERIAL</p> + + +<p>The observational material on line-intensities follows in tabular form. +The measures were made in two groups, comprising respectively the +hotter stars and the stars cooler than Class \(A_0\), and different +intensity scales were used for the two. The solar scale mentioned above +was used for the second group of stars; the first group was referred +<span class="pagenum" id="Page_119">[Pg 119]</span> +to standard lines in the spectrum of \(\alpha\) Cygni. The distribution +of the stars in the two groups among the spectral classes was as +follows:</p> + +<table class="autotable"> +<thead><tr> +<th class="tdc">Group I</th> +<th class="tdc">\(B_0\)</th> +<th class="tdc">\(B_1\)</th> +<th class="tdc">\(B_2\)</th> +<th class="tdc">\(B_3\)</th> +<th class="tdc">\(B_5\)</th> +<th class="tdc">\(B_8\)</th> +<th class="tdc">\(B_9\)</th> +<th class="tdc">\(A_0\)</th> +</tr> +</thead> +<tbody><tr> +<td class="tdl">giants</td> +<td class="tdr">4</td> +<td class="tdr">7</td> +<td class="tdr">7</td> +<td class="tdr">6</td> +<td class="tdr">8</td> +<td class="tdr">6</td> +<td class="tdr">3</td> +<td class="tdr">17</td> +</tr><tr> +<td class="tdl">super-giants</td> +<td class="tdr">-</td> +<td class="tdr">-</td> +<td class="tdr">-</td> +<td class="tdr">-</td> +<td class="tdr">2</td> +<td class="tdr">1</td> +<td class="tdr">-</td> +<td class="tdr">-</td> +</tr> + </tbody> +</table> + +<table class="autotable"> +<thead><tr> +<th class="tdc_ws1">Group II</th> +<th class="tdc_ws1">\(B_9\)</th> +<th class="tdc_ws1">\(A_0\)</th> +<th class="tdc_ws1">\(A_2\)</th> +<th class="tdc_ws1">\(A_3\)</th> +<th class="tdc_ws1">\(A_5\)</th> +<th class="tdc_ws1">\(F_0\)</th> +<th class="tdc_ws1">\(F_2\)</th> +<th class="tdc_ws1">\(F_5\)</th> +<th class="tdc_ws1">\(F_8\)</th> +<th class="tdc_ws1">\(G_0\)</th> +<th class="tdc_ws1">\(G_5\)</th> +<th class="tdc_ws1">\(K_0\)</th> +<th class="tdc_ws1">\(K_2\)</th> +<th class="tdc_ws1">\(K_5\)</th> +<th class="tdc_ws1">\(M_a\)</th> +<th class="tdc_ws1">\(M_b\)</th> +<th class="tdc_ws1">\(M_d\)</th> +</tr> +</thead> +<tbody><tr> +<td class="tdl_ws1">dwarfs</td> +<td class="tdr">-</td> +<td class="tdr">-</td> +<td class="tdr">-</td> +<td class="tdr">-</td> +<td class="tdr">-</td> +<td class="tdr">4</td> +<td class="tdr">1</td> +<td class="tdr">2</td> +<td class="tdr">3</td> +<td class="tdr">2</td> +<td class="tdr">2</td> +<td class="tdr">-</td> +<td class="tdr">-</td> +<td class="tdr">-</td> +<td class="tdr">-</td> +<td class="tdr">-</td> +<td class="tdr">-</td> +</tr><tr> +<td class="tdl_ws1">giants</td> +<td class="tdr">1</td> +<td class="tdr">9</td> +<td class="tdr">3</td> +<td class="tdr">5</td> +<td class="tdr">2</td> +<td class="tdr">-</td> +<td class="tdr">-</td> +<td class="tdr">-</td> +<td class="tdr">-</td> +<td class="tdr">3</td> +<td class="tdr">5</td> +<td class="tdr">20</td> +<td class="tdr">4</td> +<td class="tdr">8</td> +<td class="tdr">1</td> +<td class="tdr">5</td> +<td class="tdr">1</td> +</tr><tr> +<td class="tdl_ws1">super-giants</td> +<td class="tdr">-</td> +<td class="tdr">-</td> +<td class="tdr">-</td> +<td class="tdr">-</td> +<td class="tdr">-</td> +<td class="tdr">3</td> +<td class="tdr">1</td> +<td class="tdr">5</td> +<td class="tdr">1</td> +<td class="tdr">2</td> +<td class="tdr">-</td> +<td class="tdr">2?</td> +<td class="tdr">1?</td> +<td class="tdr">1?</td> +<td class="tdr">3</td> +<td class="tdr">1</td> +<td class="tdr">-</td> +</tr> + </tbody> +</table> + +<p>If it were possible to use a series of giants throughout, the task of +determining the intensity maxima would be greatly simplified. Among +the hotter stars the differences introduced by absolute magnitude +are not great enough to make the maxima difficult to determine. With +later classes, however, the changes with absolute magnitude are very +marked. As will be pointed out in an ensuing chapter,<a id="FNanchor_406" href="#Footnote_406" class="fnanchor">[406]</a> the actual +strength of the lines differs considerably from giant to dwarf, owing +to the difference in the effective optical depth of the photosphere. +This difference in strength is in addition to the well-known “absolute +magnitude effect” which is shown, for example, by the enhanced lines; +it increases the difficulty of making estimates of line change from one +class to the next, since, owing to selection, the available stars are +far from homogeneous in absolute magnitude. In addition to this factor, +there is the practical difficulty of making comparable estimates on the +sharp narrow lines of a super-giant and those of a dwarf, since the +lines of a dwarf tend to be hazy and lack contrast with the background.</p> + +<p>It might be expected, from the distribution in luminosity of the +stars used, that irregularities in the intensity sequence would +probably occur in the \(F\) classes and at \(M_a\). For the purpose +of estimation of maxima, the \(F\) classes are not of very great +importance, as few of the maxima under present investigation occur +there, but the irregularity at \(M_a\) may well prove to be serious. +<span class="pagenum" id="Page_120">[Pg 120]</span> +There is indeed a general tendency for the intensity of, metallic lines +to increase at \(M_a\). All the \(M_a\) stars measured were of very +high luminosity, and probably the rise of intensity is due to this +feature, or rather to the increase of material above the photosphere +that accompanies it. A maximum is only assumed to occur at \(M_a\) when +a line increases regularly through the \(K\) types, as do the lines of +neutral calcium. The iron and titanium maxima obviously occur earlier +in the sequence, although the lines of both these elements are often +noticeably strengthened at \(M_a\).</p> + +<p>The following tabulation contains the data on line-intensity for all +the lines of known series relations that have been measured up to the +present. All the measures were made by the writer, excepting those for +zinc, which are taken from Menzel’s paper.<a id="FNanchor_407" href="#Footnote_407" class="fnanchor">[407]</a> Successive columns of +the table contain the atom, the series relations, the wave-length, and +the observed intensities in the various spectral classes. The column +headed “Blends” is a direct transcription from Rowland’s tables, and +contains details both of the line under consideration and of closely +adjacent lines. The column headed “Remarks” contains the writer’s own +conclusions, based on solar evidence, astrophysical behavior, and +laboratory affinities, as to the source and maximum of the line that +has been measured.</p> + +<p><span class="pagenum" id="Page_121">[Pg 121]</span></p> + +<p>The recorded intensities, for classes cooler than \(B_0\), are derived +from the selection of stars mentioned earlier in the present chapter. A +list of the individual stars is contained in <a href="#APPENDIX_III">Appendix III</a>. Four typical +\(O\) stars have been selected to represent that class. The figures in the +final column refer to the notes to the table, which are listed under +the respective atoms, and give the observed maximum, the intensities +and origins of blended lines (in Rowland’s notation), and short +remarks, which indicate whether or no the observed behavior is to be +attributed to the line considered. Maxima that are obviously due to +another line are placed in parentheses.</p> + +<h2><a id="TABLE_XIX">TABLE XIX</a></h2> + +<table class="autotable"> +<thead><tr> +<th class="tdc bb bt2 br">Atom</th> +<th class="tdc bb bt2 br">\(\lambda\)</th> +<th class="tdc bb bt2 br"> Series </th> +<th class="tdc bb bt2">\(B_9\)</th> +<th class="tdc bb bt2">\(A_0\)</th> +<th class="tdc bb bt2">\(A_2\)</th> +<th class="tdc bb bt2">\(A_3\)</th> +<th class="tdc bb bt2">\(A_5\)</th> +<th class="tdc bb bt2">\(F_0\)</th> +<th class="tdc bb bt2">\(F_5\)</th> +<th class="tdc bb bt2">\(F_8\)</th> +<th class="tdc bb bt2">\(G_0\)</th> +<th class="tdc bb bt2">\(G_5\)</th> +<th class="tdc bb bt2">\(K_0\)</th> +<th class="tdc bb bt2">\(K_2\)</th> +<th class="tdc bb bt2">\(K_5\)</th> +<th class="tdc bb bt2">\(M_a\)</th> +<th class="tdc bb bt2 br">\(M_b\)</th> +<th class="tdc bb bt2">Notes</th> +</tr> +</thead> +<tbody><tr> +<td class="tdl br">H</td> +<td class="tdc br">3970.1</td> +<td class="tdc br">\(_2P-_7D\)</td> +<td class="tdc">20.0</td> +<td class="tdc">17.6</td> +<td class="tdc">20.0</td> +<td class="tdc">15.6</td> +<td class="tdc">15.0</td> +<td class="tdc">17.2</td> +<td class="tdc">17.8</td> +<td class="tdc">..</td> +<td class="tdc">18.0</td> +<td class="tdc">20.0</td> +<td class="tdc">24.5</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">30.0</td> +<td class="tdc br">..</td> +<td class="tdr"><a href="#1a">1</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4101.7</td> +<td class="tdc br">\(_2P-_6D\)</td> +<td class="tdc">18.0</td> +<td class="tdc">16.0</td> +<td class="tdc">16.3</td> +<td class="tdc">13.6</td> +<td class="tdc">15.0</td> +<td class="tdc">13.9</td> +<td class="tdc">10.7</td> +<td class="tdc">10.6</td> +<td class="tdc">9.4</td> +<td class="tdc">7.0</td> +<td class="tdc">7.0</td> +<td class="tdc">7.0</td> +<td class="tdc">7.3</td> +<td class="tdc">9.0</td> +<td class="tdc br">6.0</td> +<td class="tdr"><a href="#2a">2</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4340.5</td> +<td class="tdc br">\(_2P-_5D\)</td> +<td class="tdc">..</td> +<td class="tdc">16.0</td> +<td class="tdc">14.3</td> +<td class="tdc">12.2</td> +<td class="tdc">14.6</td> +<td class="tdc">13.2</td> +<td class="tdc">10.8</td> +<td class="tdc">9.2</td> +<td class="tdc">9.4</td> +<td class="tdc">9.0</td> +<td class="tdc">8.7</td> +<td class="tdc">8.4</td> +<td class="tdc">9.2</td> +<td class="tdc">9.6</td> +<td class="tdc br">9.0</td> +<td class="tdr"><a href="#3a">3</a></td> +</tr><tr> +<td class="tdl bb br"></td> +<td class="tdc bb br">4861.3</td> +<td class="tdc bb br">\(_2P-_4D\)</td> +<td class="tdc bb">15.0</td> +<td class="tdc bb">14.0</td> +<td class="tdc bb">14.0</td> +<td class="tdc bb">14.6</td> +<td class="tdc bb">13.3</td> +<td class="tdc bb">12.3</td> +<td class="tdc bb">11.0</td> +<td class="tdc bb">9.0</td> +<td class="tdc bb">8.5</td> +<td class="tdc bb">7.6</td> +<td class="tdc bb">6.6</td> +<td class="tdc bb">5.6</td> +<td class="tdc bb">5.1</td> +<td class="tdc bb">6.7</td> +<td class="tdc bb br">4.0</td> +<td class="tdr bb"><a href="#4a">4</a></td> +</tr><tr> +<td class="tdc bb br"></td> +<td class="tdc bb br"></td> +<td class="tdc bb br"></td> +<td class="tdc bb">\(\xi~Pup\)</td> +<td class="tdc bb">\(\delta~Cir\)</td> +<td class="tdc bb">\(_{29}CM_a\)</td> +<td class="tdc bb">\(\tau~CM_a\)</td> +<td class="tdc bb">\(B_0\)</td> +<td class="tdc bb">\(B_1\)</td> +<td class="tdc bb">\(B_2\)</td> +<td class="tdc bb">\(B_3\)</td> +<td class="tdc bb">\(B_5\)</td> +<td class="tdc bb">\(B_8\)</td> +<td class="tdc bb">\(B_9\)</td> +<td class="tdc bb">\(A_0\)</td> +<td class="tdc bb">\(A_2\)</td> +<td class="tdc bb">\(A_3\)</td> +<td class="tdc bb br">\(A_5\)</td> +<td class="tdc bb"></td> +</tr><tr> +<td class="tdl br">He</td> +<td class="tdc br">4713.4</td> +<td class="tdc br">\(1^2P-3^2S\)</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">6.5</td> +<td class="tdc">8.2</td> +<td class="tdc">7.5</td> +<td class="tdc">6.0</td> +<td class="tdc">6.7</td> +<td class="tdc">4.2</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc br">0.0</td> +<td class="tdr"><a href="#1b">1</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4713.1</td> +<td class="tdc br">\(1^2P-3^2S\)</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc br"></td> +<td class="tdr"></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4121.0</td> +<td class="tdc br">\(1^2P-4^2S\)</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">8.5</td> +<td class="tdc">9.5</td> +<td class="tdc">11.0</td> +<td class="tdc">9.2</td> +<td class="tdc">6.4</td> +<td class="tdc">4.2</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc br">0.0</td> +<td class="tdr"><a href="#2b">2</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4120.9</td> +<td class="tdc br">\(1^2P-4^2S\)</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc br"></td> +<td class="tdr"></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4471.7</td> +<td class="tdc br">\(1^2P-3^2D\)</td> +<td class="tdc">..</td> +<td class="tdc">6.5</td> +<td class="tdc">8.5</td> +<td class="tdc">8.0</td> +<td class="tdc">11.0</td> +<td class="tdc">11.5</td> +<td class="tdc">11.6</td> +<td class="tdc">11.8</td> +<td class="tdc">11.1</td> +<td class="tdc">9.7</td> +<td class="tdc">8.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc br">0.0</td> +<td class="tdr"><a href="#3b">3</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4471.5</td> +<td class="tdc br">\(1^2P-3^2D\)</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc br"></td> +<td class="tdr"></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4026.4</td> +<td class="tdc br">\(1^2P-4^2D\)</td> +<td class="tdc">4.0</td> +<td class="tdc">6.9</td> +<td class="tdc">9.0</td> +<td class="tdc">8.0</td> +<td class="tdc">12.0</td> +<td class="tdc">12.7</td> +<td class="tdc">14.0</td> +<td class="tdc">15.4</td> +<td class="tdc">12.0</td> +<td class="tdc">10.8</td> +<td class="tdc">8.5</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc br">0.0</td> +<td class="tdr"><a href="#4b">4</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4026.2</td> +<td class="tdc br">\(1^2P-4^2D\)</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc br"></td> +<td class="tdr"></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4921.9</td> +<td class="tdc br">\(_1P-_3D\)</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">10.0</td> +<td class="tdc">12.4</td> +<td class="tdc">10.7</td> +<td class="tdc">10.0</td> +<td class="tdc">10.0</td> +<td class="tdc">7.0</td> +<td class="tdc">4.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc br">0.0</td> +<td class="tdr"><a href="#5b">5</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4387.9</td> +<td class="tdc br">\(_1P-_4D\)</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">4.0</td> +<td class="tdc">4.0</td> +<td class="tdc">10.0</td> +<td class="tdc">10.3</td> +<td class="tdc">11.0</td> +<td class="tdc">11.5</td> +<td class="tdc">9.2</td> +<td class="tdc">..</td> +<td class="tdc">4.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc br">0.0</td> +<td class="tdr"><a href="#6b">6</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4143.8</td> +<td class="tdc br">\(_1P-_5D\)</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">5.0</td> +<td class="tdc">4.0</td> +<td class="tdc">9.6</td> +<td class="tdc">10.0</td> +<td class="tdc">10.7</td> +<td class="tdc">12.0</td> +<td class="tdc">7.5</td> +<td class="tdc">4.9</td> +<td class="tdc">3.5</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc br">0.0</td> +<td class="tdr"><a href="#7b">7</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4009.3</td> +<td class="tdc br">\(_1P-_6D\)</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">7.0</td> +<td class="tdc">9.1</td> +<td class="tdc">10.2</td> +<td class="tdc">11.4</td> +<td class="tdc">5.8</td> +<td class="tdc">4.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc br">0.0</td> +<td class="tdr"><a href="#8b">8</a></td> +</tr><tr> +<td class="tdl br">He+</td> +<td class="tdc br">4685.8</td> +<td class="tdc br">\(_3D-_4F\)</td> +<td class="tdc">em.</td> +<td class="tdc">5.8</td> +<td class="tdc">em.</td> +<td class="tdc">6.0</td> +<td class="tdc">4.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc br">0.0</td> +<td class="tdr"><a href="#9b">9</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4541.6</td> +<td class="tdc br">\(_4F-_9G\)</td> +<td class="tdc">6.0</td> +<td class="tdc">5.3</td> +<td class="tdc">5.5</td> +<td class="tdc">6.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc br">0.0</td> +<td class="tdr"><a href="#10b">10</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4199.9</td> +<td class="tdc br">\(_4F-_{11}G\)</td> +<td class="tdc">5.0</td> +<td class="tdc">3.5</td> +<td class="tdc">6.1</td> +<td class="tdc">5.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc br">0.0</td> +<td class="tdr"><a href="#11b">11</a></td> +</tr><tr> +<td class="tdl bb br"></td> +<td class="tdc bb br">4025.6</td> +<td class="tdc bb br">\(_4F-_{13}G\)</td> +<td class="tdc bb">4.0</td> +<td class="tdc bb">6.9</td> +<td class="tdc bb">9.0</td> +<td class="tdc bb">8.0</td> +<td class="tdc bb">0.0</td> +<td class="tdc bb">0.0</td> +<td class="tdc bb">0.0</td> +<td class="tdc bb">0.0</td> +<td class="tdc bb">0.0</td> +<td class="tdc bb">0.0</td> +<td class="tdc bb">0.0</td> +<td class="tdc bb">0.0</td> +<td class="tdc bb">0.0</td> +<td class="tdc bb">0.0</td> +<td class="tdc bb br">0.0</td> +<td class="tdr bb"><a href="#12b">12</a></td> +</tr><tr> +<td class="tdl bb br">C+</td> +<td class="tdc bb br">4267</td> +<td class="tdc bb br">\(3^2D-^2F\)</td> +<td class="tdc bb">0.0</td> +<td class="tdc bb">0.0</td> +<td class="tdc bb">0.0</td> +<td class="tdc bb">0.0</td> +<td class="tdc bb">5.0</td> +<td class="tdc bb">7.4</td> +<td class="tdc bb">7.7</td> +<td class="tdc bb">8.0</td> +<td class="tdc bb">7.8</td> +<td class="tdc bb">4.5</td> +<td class="tdc bb">3.0</td> +<td class="tdc bb">0.0</td> +<td class="tdc bb">0.0</td> +<td class="tdc bb">0.0</td> +<td class="tdc bb br">0.0</td> +<td class="tdr bb"><a href="#1c">1</a><span class="pagenum" id="Page_122">[Pg 122]</span></td> +</tr><tr> +<td class="tdl br">Mg</td> +<td class="tdc br">5183.7</td> +<td class="tdc br"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc br"></td> +<td class="tdr"></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">5172.7</td> +<td class="tdc br">\(1^3P-1^3S\)</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">8.0</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">8.0</td> +<td class="tdc">8.0</td> +<td class="tdc">8.0</td> +<td class="tdc">10.0</td> +<td class="tdc">8.0</td> +<td class="tdc">10.0</td> +<td class="tdc br">..</td> +<td class="tdr"><a href="#1d">1</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">5167.4</td> +<td class="tdc br"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc br"></td> +<td class="tdr"></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4571.1</td> +<td class="tdc br">\(_1S-1^2P\)</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">2.0</td> +<td class="tdc">3.5</td> +<td class="tdc">5.2</td> +<td class="tdc">3.3</td> +<td class="tdc">6.4</td> +<td class="tdc">5.8</td> +<td class="tdc">6.2</td> +<td class="tdc">6.8</td> +<td class="tdc">6.9</td> +<td class="tdc">7.0</td> +<td class="tdc br">6.1</td> +<td class="tdr"><a href="#2d">2</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4351.9</td> +<td class="tdc br">\(_1P-_5D\)</td> +<td class="tdc">..</td> +<td class="tdc">2.0</td> +<td class="tdc">4.0</td> +<td class="tdc">5.0</td> +<td class="tdc">4.3</td> +<td class="tdc">6.3</td> +<td class="tdc">7.4</td> +<td class="tdc">5.0</td> +<td class="tdc">7.3</td> +<td class="tdc">8.1</td> +<td class="tdc">8.0</td> +<td class="tdc">7.0</td> +<td class="tdc">8.1</td> +<td class="tdc">8.6</td> +<td class="tdc br">9.0</td> +<td class="tdr"><a href="#3d">3</a></td> +</tr><tr> +<td class="tdl br">Mg+</td> +<td class="tdc br">4481.3</td> +<td class="tdc br">\(2^2D-3^2F\)</td> +<td class="tdc">5.0</td> +<td class="tdc">4.6</td> +<td class="tdc">6.0</td> +<td class="tdc">5.5</td> +<td class="tdc">6.7</td> +<td class="tdc">8.0</td> +<td class="tdc">7.2</td> +<td class="tdc">8.1</td> +<td class="tdc">8.3</td> +<td class="tdc">8.6</td> +<td class="tdc">9.0</td> +<td class="tdc">7.7</td> +<td class="tdc">8.0</td> +<td class="tdc">9.4</td> +<td class="tdc br">7.6</td> +<td class="tdr"><a href="#4d">4</a></td> +</tr><tr> +<td class="tdl bb br"></td> +<td class="tdc bb br">4481.1</td> +<td class="tdc bb br">\(2^2D-3^2F\)</td> +<td class="tdc bb"></td> +<td class="tdc bb"></td> +<td class="tdc bb"></td> +<td class="tdc bb"></td> +<td class="tdc bb"></td> +<td class="tdc bb"></td> +<td class="tdc bb"></td> +<td class="tdc bb"></td> +<td class="tdc bb"></td> +<td class="tdc bb"></td> +<td class="tdc bb"></td> +<td class="tdc bb"></td> +<td class="tdc bb"></td> +<td class="tdc bb"></td> +<td class="tdc bb br"></td> +<td class="tdr bb"></td> +</tr><tr> +<td class="tdl br">Al</td> +<td class="tdc br">3961.3</td> +<td class="tdc br">\(1^2P-1^2S\)</td> +<td class="tdc">..</td> +<td class="tdc">tr.</td> +<td class="tdc">2.0</td> +<td class="tdc">5.3</td> +<td class="tdc">..</td> +<td class="tdc">5.7</td> +<td class="tdc">5.5</td> +<td class="tdc">..</td> +<td class="tdc">8.3</td> +<td class="tdc">8.0</td> +<td class="tdc">8.5</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">9.0</td> +<td class="tdc br">11.0</td> +<td class="tdr"><a href="#1e">1</a></td> +</tr><tr> +<td class="tdl bb br"></td> +<td class="tdc bb br">3944.0</td> +<td class="tdc bb br">\(1^2P-1^2S\)</td> +<td class="tdc bb">..</td> +<td class="tdc bb">tr.</td> +<td class="tdc bb">2.0</td> +<td class="tdc bb">6.0</td> +<td class="tdc bb">..</td> +<td class="tdc bb">5.2</td> +<td class="tdc bb">6.0</td> +<td class="tdc bb">8.0</td> +<td class="tdc bb">8.0</td> +<td class="tdc bb">8.3</td> +<td class="tdc bb">8.5</td> +<td class="tdc bb">..</td> +<td class="tdc bb">..</td> +<td class="tdc bb">8.5</td> +<td class="tdc bb br">11.0</td> +<td class="tdr bb"><a href="#2e">2</a></td> +</tr><tr> +<td class="tdl bb br">Si</td> +<td class="tdc bb br">3905</td> +<td class="tdc bb br"></td> +<td class="tdc bb">..</td> +<td class="tdc bb">..</td> +<td class="tdc bb">2.0</td> +<td class="tdc bb">..</td> +<td class="tdc bb">4.0</td> +<td class="tdc bb">8.8</td> +<td class="tdc bb">9.3</td> +<td class="tdc bb">11.5</td> +<td class="tdc bb">11.7</td> +<td class="tdc bb">11.4</td> +<td class="tdc bb">11.3</td> +<td class="tdc bb">10.0</td> +<td class="tdc bb">10.0</td> +<td class="tdc bb">9.6</td> +<td class="tdc bb br">8.6</td> +<td class="tdr bb"><a href="#1f">1</a></td> +</tr><tr> +<td class="tdc bb br"></td> +<td class="tdc bb br"></td> +<td class="tdc bb br"></td> +<td class="tdc bb">\(\xi~Pup\)</td> +<td class="tdc bb">\(\delta~Cir\)</td> +<td class="tdc bb">\(_{29}CM_a\)</td> +<td class="tdc bb">\(\tau~CM_a\)</td> +<td class="tdc bb">\(B_0\)</td> +<td class="tdc bb">\(B_1\)</td> +<td class="tdc bb">\(B_2\)</td> +<td class="tdc bb">\(B_3\)</td> +<td class="tdc bb">\(B_5\)</td> +<td class="tdc bb">\(B_8\)</td> +<td class="tdc bb">\(B_9\)</td> +<td class="tdc bb">\(A_0\)</td> +<td class="tdc bb">\(A_2\)</td> +<td class="tdc bb">\(A_3\)</td> +<td class="tdc bb br">\(A_5\)</td> +<td class="tdc bb"></td> +</tr><tr> +<td class="tdl br">Si+</td> +<td class="tdc br">4131</td> +<td class="tdc br"></td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">2.0</td> +<td class="tdc">3.0</td> +<td class="tdc">2.7</td> +<td class="tdc">3.5</td> +<td class="tdc">4.4</td> +<td class="tdc">3.6</td> +<td class="tdc">6.2</td> +<td class="tdc">9.3</td> +<td class="tdc">7.0</td> +<td class="tdc">..</td> +<td class="tdc br">..</td> +<td class="tdr"><a href="#2f">2</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4128</td> +<td class="tdc br"></td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">2.0</td> +<td class="tdc">3.0</td> +<td class="tdc">2.7</td> +<td class="tdc">3.5</td> +<td class="tdc">4.4</td> +<td class="tdc">3.6</td> +<td class="tdc">6.2</td> +<td class="tdc">9.3</td> +<td class="tdc">7.0</td> +<td class="tdc">..</td> +<td class="tdc br">..</td> +<td class="tdr"></td> +</tr><tr> +<td class="tdl br">Si++</td> +<td class="tdc br">4574</td> +<td class="tdc br"></td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">3.0</td> +<td class="tdc">8.0</td> +<td class="tdc">8.0</td> +<td class="tdc">2.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc br">0.0</td> +<td class="tdr"><a href="#3f">3</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4568</td> +<td class="tdc br"></td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">2.0</td> +<td class="tdc">9.0</td> +<td class="tdc">9.0</td> +<td class="tdc">4.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc br">0.0</td> +<td class="tdr"><a href="#4f">4</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4552</td> +<td class="tdc br"></td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">5.0</td> +<td class="tdc">10.0</td> +<td class="tdc">10.0</td> +<td class="tdc">5.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc br">0.0</td> +<td class="tdr"><a href="#5f">5</a></td> +</tr><tr> +<td class="tdl br">Si+++</td> +<td class="tdc br">4116</td> +<td class="tdc br"></td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">5.0</td> +<td class="tdc">6.0</td> +<td class="tdc">8.3</td> +<td class="tdc">4.7</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc br">0.0</td> +<td class="tdr"><a href="#6f">6</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4096</td> +<td class="tdc br"></td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">8.7</td> +<td class="tdc">6.0</td> +<td class="tdc">9.7</td> +<td class="tdc">5.2</td> +<td class="tdc">3.6</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc br">0.0</td> +<td class="tdr"><a href="#7f">7</a></td> +</tr><tr> +<td class="tdl bb br"></td> +<td class="tdc bb br">4089</td> +<td class="tdc bb br"></td> +<td class="tdc bb">..</td> +<td class="tdc bb">..</td> +<td class="tdc bb">7.5</td> +<td class="tdc bb">8.0</td> +<td class="tdc bb">9.2</td> +<td class="tdc bb">5.5</td> +<td class="tdc bb">5.2</td> +<td class="tdc bb">0.0</td> +<td class="tdc bb">0.0</td> +<td class="tdc bb">0.0</td> +<td class="tdc bb">0.0</td> +<td class="tdc bb">0.0</td> +<td class="tdc bb">0.0</td> +<td class="tdc bb">0.0</td> +<td class="tdc bb br">0.0</td> +<td class="tdr bb"><a href="#8f">8</a></td> +</tr><tr> +<td class="tdc bb br"></td> +<td class="tdc bb br"></td> +<td class="tdc bb br"></td> +<td class="tdc bb">\(B_9\)</td> +<td class="tdc bb">\(A_0\)</td> +<td class="tdc bb">\(A_2\)</td> +<td class="tdc bb">\(A_3\)</td> +<td class="tdc bb">\(A_5\)</td> +<td class="tdc bb">\(F_0\)</td> +<td class="tdc bb">\(F_5\)</td> +<td class="tdc bb">\(F_8\)</td> +<td class="tdc bb">\(G_0\)</td> +<td class="tdc bb">\(G_5\)</td> +<td class="tdc bb">\(K_0\)</td> +<td class="tdc bb">\(K_2\)</td> +<td class="tdc bb">\(K_5\)</td> +<td class="tdc bb">\(M_a\)</td> +<td class="tdc bb br">\(M_b\)</td> +<td class="tdc bb"></td> +</tr><tr> +<td class="tdl br">Ca</td> +<td class="tdc br">4581.4</td> +<td class="tdc br">\(1^3D-3^3F\)</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">3.0</td> +<td class="tdc">2.5</td> +<td class="tdc">4.2</td> +<td class="tdc">6.7</td> +<td class="tdc">5.0</td> +<td class="tdc">7.7</td> +<td class="tdc">8.1</td> +<td class="tdc">7.8</td> +<td class="tdc">8.0</td> +<td class="tdc">7.1</td> +<td class="tdc">8.3</td> +<td class="tdc br">6.2</td> +<td class="tdr"><a href="#1g">1</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4454.8</td> +<td class="tdc br">\(1^2P-2^3D\)</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">3.0</td> +<td class="tdc">5.0</td> +<td class="tdc">2.6</td> +<td class="tdc">5.0</td> +<td class="tdc">6.2</td> +<td class="tdc">6.0</td> +<td class="tdc">5.1</td> +<td class="tdc">5.0</td> +<td class="tdc">4.8</td> +<td class="tdc">4.4</td> +<td class="tdc">5.6</td> +<td class="tdc br">5.0</td> +<td class="tdr"><a href="#2g">2</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4434.9</td> +<td class="tdc br">\(1^3P-2^3D\)</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">4.0</td> +<td class="tdc">4.3</td> +<td class="tdc">5.2</td> +<td class="tdc">6.2</td> +<td class="tdc">6.0</td> +<td class="tdc">7.5</td> +<td class="tdc">7.6</td> +<td class="tdc">7.9</td> +<td class="tdc">9.2</td> +<td class="tdc">8.8</td> +<td class="tdc">9.7</td> +<td class="tdc br">9.3</td> +<td class="tdr"><a href="#3g">3</a><span class="pagenum" id="Page_123">[Pg 123]</span></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4307.7</td> +<td class="tdc br">\(1^3P-^3P'\)</td> +<td class="tdc">0.0</td> +<td class="tdc">3.3</td> +<td class="tdc">3.0</td> +<td class="tdc">4.4</td> +<td class="tdc">3.6</td> +<td class="tdc">4.9</td> +<td class="tdc">6.5</td> +<td class="tdc">7.2</td> +<td class="tdc">9.5</td> +<td class="tdc">8.6</td> +<td class="tdc">8.6</td> +<td class="tdc">10.3</td> +<td class="tdc">10.5</td> +<td class="tdc">12.0</td> +<td class="tdc br">13.1</td> +<td class="tdr"><a href="#4g">4</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4302.5</td> +<td class="tdc br">\(1^3P-^3P'\)</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">..</td> +<td class="tdc">8.0</td> +<td class="tdc">..</td> +<td class="tdc">3.5</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">5.5</td> +<td class="tdc">..</td> +<td class="tdc">4.0</td> +<td class="tdc">4.5</td> +<td class="tdc">5.0</td> +<td class="tdc br">8.0</td> +<td class="tdr"><a href="#5g">5</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4299.0</td> +<td class="tdc br">\(1^3P-^3P'\)</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">3.0</td> +<td class="tdc">5.2</td> +<td class="tdc">5.0</td> +<td class="tdc">6.8</td> +<td class="tdc">7.4</td> +<td class="tdc">6.5</td> +<td class="tdc">6.6</td> +<td class="tdc">8.0</td> +<td class="tdc">8.0</td> +<td class="tdc">8.6</td> +<td class="tdc">7.9</td> +<td class="tdc">..</td> +<td class="tdc br">6.0</td> +<td class="tdr"><a href="#6g">6</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4289.4</td> +<td class="tdc br">\(1^3P-^3P'\)</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">3.0</td> +<td class="tdc">4.4</td> +<td class="tdc">4.6</td> +<td class="tdc">7.6</td> +<td class="tdc">7.8</td> +<td class="tdc">6.7</td> +<td class="tdc">8.2</td> +<td class="tdc">7.4</td> +<td class="tdc">7.7</td> +<td class="tdc">8.6</td> +<td class="tdc">9.3</td> +<td class="tdc">11.4</td> +<td class="tdc br">10.5</td> +<td class="tdr"><a href="#7g">7</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4283.0</td> +<td class="tdc br">\(1^3P-^3P'\)</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">..</td> +<td class="tdc">5.0</td> +<td class="tdc">3.0</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">4.0</td> +<td class="tdc">5.0</td> +<td class="tdc">6.1</td> +<td class="tdc">5.0</td> +<td class="tdc">6.0</td> +<td class="tdc">8.0</td> +<td class="tdc br">4.4</td> +<td class="tdr"><a href="#8g">8</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4226.7</td> +<td class="tdc br">\(_1S-_1P\)</td> +<td class="tdc">3.0</td> +<td class="tdc">2.3</td> +<td class="tdc">3.0</td> +<td class="tdc">5.8</td> +<td class="tdc">6.3</td> +<td class="tdc">7.9</td> +<td class="tdc">9.3</td> +<td class="tdc">8.6</td> +<td class="tdc">10.4</td> +<td class="tdc">9.7</td> +<td class="tdc">11.7</td> +<td class="tdc">13.6</td> +<td class="tdc">14.5</td> +<td class="tdc">14.2</td> +<td class="tdc br">16.0</td> +<td class="tdr"><a href="#9g">9</a></td> +</tr><tr> +<td class="tdl br">Ca+</td> +<td class="tdc br">3968.5</td> +<td class="tdc br">\(1^2S-1^2P\)</td> +<td class="tdc">20.0</td> +<td class="tdc">17.6</td> +<td class="tdc">20.0</td> +<td class="tdc">15.6</td> +<td class="tdc">15.0</td> +<td class="tdc">17.2</td> +<td class="tdc">17.8</td> +<td class="tdc">20.0</td> +<td class="tdc">18.0</td> +<td class="tdc">20.0</td> +<td class="tdc">24.5</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">30.0</td> +<td class="tdc br">..</td> +<td class="tdr"><a href="#10g">10</a></td> +</tr><tr> +<td class="tdl bb br"></td> +<td class="tdc bb br">3933.7</td> +<td class="tdc bb br">\(1^2S-1^2P\)</td> +<td class="tdc bb">5.0</td> +<td class="tdc bb">10.3</td> +<td class="tdc bb">13.3</td> +<td class="tdc bb">13.8</td> +<td class="tdc bb">15.0</td> +<td class="tdc bb">17.1</td> +<td class="tdc bb">20.0</td> +<td class="tdc bb">20.0</td> +<td class="tdc bb">19.6</td> +<td class="tdc bb">20.0</td> +<td class="tdc bb">21.5</td> +<td class="tdc bb">..</td> +<td class="tdc bb">..</td> +<td class="tdc bb">30.0</td> +<td class="tdc bb br">..</td> +<td class="tdr bb"><a href="#11g">11</a></td> +</tr><tr> +<td class="tdl br">Sc+</td> +<td class="tdc br">4246.8</td> +<td class="tdc br">\(^3F-^3D'\)</td> +<td class="tdc">0.0</td> +<td class="tdc">3.0</td> +<td class="tdc">2.0</td> +<td class="tdc">6.0</td> +<td class="tdc">5.0</td> +<td class="tdc">6.0</td> +<td class="tdc">7.0</td> +<td class="tdc">5.0</td> +<td class="tdc">6.3</td> +<td class="tdc">5.6</td> +<td class="tdc">5.3</td> +<td class="tdc">5.6</td> +<td class="tdc">5.4</td> +<td class="tdc">8.6</td> +<td class="tdc br">6.8</td> +<td class="tdr"><a href="#1h">1</a></td> +</tr><tr> +<td class="tdl bb br"></td> +<td class="tdc bb br">4320.8</td> +<td class="tdc bb br">\(^3F-^3D'\)</td> +<td class="tdc bb">0.0</td> +<td class="tdc bb">0.0</td> +<td class="tdc bb">0.0</td> +<td class="tdc bb">0.0</td> +<td class="tdc bb">0.0</td> +<td class="tdc bb">3.8</td> +<td class="tdc bb">5.5</td> +<td class="tdc bb">4.0</td> +<td class="tdc bb">4.0</td> +<td class="tdc bb">3.5</td> +<td class="tdc bb">3.8</td> +<td class="tdc bb">4.5</td> +<td class="tdc bb">4.0</td> +<td class="tdc bb">5.0</td> +<td class="tdc bb br">4.0</td> +<td class="tdr bb"><a href="#2h">2</a></td> +</tr><tr> +<td class="tdl br">Ti</td> +<td class="tdc br">4395.2</td> +<td class="tdc br">\(1^5D-^5F\)</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">3.0</td> +<td class="tdc">..</td> +<td class="tdc">6.7</td> +<td class="tdc">7.2</td> +<td class="tdc">..</td> +<td class="tdc">5.7</td> +<td class="tdc">5.7</td> +<td class="tdc">5.4</td> +<td class="tdc">6.2</td> +<td class="tdc">6.8</td> +<td class="tdc">7.2</td> +<td class="tdc br">6.5</td> +<td class="tdr"><a href="#1i">1</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4301.1</td> +<td class="tdc br">\(1^5F-^5D\)</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">8.0</td> +<td class="tdc">..</td> +<td class="tdc">3.5</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">5.5</td> +<td class="tdc">..</td> +<td class="tdc">4.0</td> +<td class="tdc">4.5</td> +<td class="tdc">5.0</td> +<td class="tdc br">8.0</td> +<td class="tdr"><a href="#2i">2</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4300.9</td> +<td class="tdc br">\(1^5F-^5D\)</td> +<td class="tdc">0.0</td> +<td class="tdc">3.0</td> +<td class="tdc">3.0</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">6.0</td> +<td class="tdc">7.6</td> +<td class="tdc">7.0</td> +<td class="tdc">5.0</td> +<td class="tdc">6.5</td> +<td class="tdc">5.0</td> +<td class="tdc">8.0</td> +<td class="tdc">5.6</td> +<td class="tdc">10.3</td> +<td class="tdc br">13.0</td> +<td class="tdr"><a href="#3i">3</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4298.7</td> +<td class="tdc br">\(1^5F-^5D\)</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">3.0</td> +<td class="tdc">5.2</td> +<td class="tdc">5.0</td> +<td class="tdc">6.8</td> +<td class="tdc">7.4</td> +<td class="tdc">6.5</td> +<td class="tdc">6.6</td> +<td class="tdc">8.0</td> +<td class="tdc">8.0</td> +<td class="tdc">8.6</td> +<td class="tdc">7.9</td> +<td class="tdc">..</td> +<td class="tdc br">6.0</td> +<td class="tdr"><a href="#4i">4</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4290.9</td> +<td class="tdc br">\(1^5F-^5D\)</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">3.0</td> +<td class="tdc">4.4</td> +<td class="tdc">4.6</td> +<td class="tdc">7.6</td> +<td class="tdc">7.8</td> +<td class="tdc">6.7</td> +<td class="tdc">8.2</td> +<td class="tdc">7.4</td> +<td class="tdc">7.7</td> +<td class="tdc">8.6</td> +<td class="tdc">9.3</td> +<td class="tdc">11.4</td> +<td class="tdc br">10.5</td> +<td class="tdr"><a href="#5i">5</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4289.1</td> +<td class="tdc br">\(1^5F-^5D\)</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc br"></td> +<td class="tdr"></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4274.6</td> +<td class="tdc br">\(1^5F-^5D\)</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">1.0</td> +<td class="tdc">3.0</td> +<td class="tdc">0.0</td> +<td class="tdc">3.5</td> +<td class="tdc">5.2</td> +<td class="tdc">5.0</td> +<td class="tdc">6.2</td> +<td class="tdc">7.2</td> +<td class="tdc">7.6</td> +<td class="tdc">9.0</td> +<td class="tdc">8.4</td> +<td class="tdc">9.5</td> +<td class="tdc br">9.4</td> +<td class="tdr"><a href="#6i">6</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">3998.7</td> +<td class="tdc br">\(1^3F-3^F_x\)</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">1.5</td> +<td class="tdc">4.5</td> +<td class="tdc">6.0</td> +<td class="tdc">5.6</td> +<td class="tdc">7.0</td> +<td class="tdc">6.0</td> +<td class="tdc">7.0</td> +<td class="tdc">7.0</td> +<td class="tdc">6.5</td> +<td class="tdc">..</td> +<td class="tdc">7.0</td> +<td class="tdc">8.0</td> +<td class="tdc br">..</td> +<td class="tdr"><a href="#7i">7</a></td> +</tr><tr> +<td class="tdl br">Ti+</td> +<td class="tdc br">4571.9</td> +<td class="tdc br">\(1^2H-1^2G'\)</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">2.0</td> +<td class="tdc">3.5</td> +<td class="tdc">5.2</td> +<td class="tdc">3.3</td> +<td class="tdc">6.4</td> +<td class="tdc">5.8</td> +<td class="tdc">6.2</td> +<td class="tdc">6.8</td> +<td class="tdc">6.9</td> +<td class="tdc">7.0</td> +<td class="tdc br">6.1</td> +<td class="tdr"><a href="#8i">8</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4563.8</td> +<td class="tdc br">\(1^2P-1^2D\)</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">2.0</td> +<td class="tdc">2.5</td> +<td class="tdc">5.2</td> +<td class="tdc">3.3</td> +<td class="tdc">6.6</td> +<td class="tdc">6.4</td> +<td class="tdc">6.7</td> +<td class="tdc">7.2</td> +<td class="tdc">6.9</td> +<td class="tdc">7.0</td> +<td class="tdc br">5.6</td> +<td class="tdr"><a href="#9i">9</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4501.3</td> +<td class="tdc br">\(1^2G-1^2F'\)</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">4.0</td> +<td class="tdc">6.6</td> +<td class="tdc">5.3</td> +<td class="tdc">6.8</td> +<td class="tdc">6.0</td> +<td class="tdc">6.4</td> +<td class="tdc">6.8</td> +<td class="tdc">7.0</td> +<td class="tdc">6.6</td> +<td class="tdc br">6.0</td> +<td class="tdr"><a href="#10i">10</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4443.8</td> +<td class="tdc br">\(2^D-^2F\)</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">5.0</td> +<td class="tdc">8.0</td> +<td class="tdc">6.9</td> +<td class="tdc">8.1</td> +<td class="tdc">7.8</td> +<td class="tdc">7.5</td> +<td class="tdc">7.6</td> +<td class="tdc">7.9</td> +<td class="tdc">9.2</td> +<td class="tdc">8.6</td> +<td class="tdc">8.0</td> +<td class="tdc br">9.0</td> +<td class="tdr"><a href="#11i">11</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4395.0</td> +<td class="tdc br">\(2^D-^2F\)</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">3.0</td> +<td class="tdc">..</td> +<td class="tdc">6.7</td> +<td class="tdc">7.2</td> +<td class="tdc">..</td> +<td class="tdc">5.7</td> +<td class="tdc">5.7</td> +<td class="tdc">5.4</td> +<td class="tdc">6.2</td> +<td class="tdc">6.8</td> +<td class="tdc">6.0</td> +<td class="tdc br">6.5</td> +<td class="tdr"><a href="#12i">12</a><span class="pagenum" id="Page_124">[Pg 124]</span></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4337.9</td> +<td class="tdc br">\(^2D-^2P_x\)</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">5.0</td> +<td class="tdc">6.3</td> +<td class="tdc">5.0</td> +<td class="tdc">7.2</td> +<td class="tdc">7.8</td> +<td class="tdc">7.2</td> +<td class="tdc">7.2</td> +<td class="tdc">8.9</td> +<td class="tdc">9.0</td> +<td class="tdc br">8.3</td> +<td class="tdr"><a href="#13i">13</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4315.0</td> +<td class="tdc br">\(^4P-^4D\)</td> +<td class="tdc">0.0</td> +<td class="tdc">3.0</td> +<td class="tdc">3.5</td> +<td class="tdc">5.0</td> +<td class="tdc">4.6</td> +<td class="tdc">6.9</td> +<td class="tdc">7.5</td> +<td class="tdc">4.6</td> +<td class="tdc">6.6</td> +<td class="tdc">5.6</td> +<td class="tdc">6.1</td> +<td class="tdc">7.0</td> +<td class="tdc">7.0</td> +<td class="tdc">8.0</td> +<td class="tdc br">8.1</td> +<td class="tdr"><a href="#14i">14</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4307.9</td> +<td class="tdc br">\(^4P-^4D\)</td> +<td class="tdc">0.0</td> +<td class="tdc">3.3</td> +<td class="tdc">3.0</td> +<td class="tdc">4.4</td> +<td class="tdc">3.6</td> +<td class="tdc">4.9</td> +<td class="tdc">6.5</td> +<td class="tdc">7.2</td> +<td class="tdc">9.5</td> +<td class="tdc">8.6</td> +<td class="tdc">8.6</td> +<td class="tdc">10.3</td> +<td class="tdc">10.5</td> +<td class="tdc">12.0</td> +<td class="tdc br">13.1</td> +<td class="tdr"><a href="#15i">15</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4301.9</td> +<td class="tdc br">\(^4P-^4D\)</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">8.0</td> +<td class="tdc">..</td> +<td class="tdc">3.5</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">5.5</td> +<td class="tdc">..</td> +<td class="tdc">4.0</td> +<td class="tdc">4.5</td> +<td class="tdc">5.0</td> +<td class="tdc br">8.0</td> +<td class="tdr"><a href="#16i">16</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4300.0</td> +<td class="tdc br">\(^4P-^4D\)</td> +<td class="tdc">0.0</td> +<td class="tdc">3.0</td> +<td class="tdc">3.0</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">6.0</td> +<td class="tdc">7.6</td> +<td class="tdc">7.0</td> +<td class="tdc">5.0</td> +<td class="tdc">6.5</td> +<td class="tdc">5.0</td> +<td class="tdc">8.0</td> +<td class="tdc">5.6</td> +<td class="tdc">10.0</td> +<td class="tdc br">13.0</td> +<td class="tdr"><a href="#17i">17</a></td> +</tr><tr> +<td class="tdl bb br"></td> +<td class="tdc bb br">4290.2</td> +<td class="tdc bb br">\(^4P-^4D\)</td> +<td class="tdc bb">0.0</td> +<td class="tdc bb">0.0</td> +<td class="tdc bb">3.0</td> +<td class="tdc bb">4.4</td> +<td class="tdc bb">4.6</td> +<td class="tdc bb">7.6</td> +<td class="tdc bb">7.8</td> +<td class="tdc bb">6.7</td> +<td class="tdc bb">8.2</td> +<td class="tdc bb">7.4</td> +<td class="tdc bb">7.7</td> +<td class="tdc bb">8.6</td> +<td class="tdc bb">9.3</td> +<td class="tdc bb">11.0</td> +<td class="tdc bb br">10.5</td> +<td class="tdr bb"><a href="#18i">18</a></td> +</tr><tr> +<td class="tdl br">V</td> +<td class="tdc br">4395.2</td> +<td class="tdc br">\(1^6D-^6F\)</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">3.0</td> +<td class="tdc">0.0</td> +<td class="tdc">6.7</td> +<td class="tdc">7.2</td> +<td class="tdc">..</td> +<td class="tdc">5.7</td> +<td class="tdc">5.7</td> +<td class="tdc">5.4</td> +<td class="tdc">6.2</td> +<td class="tdc">6.8</td> +<td class="tdc">7.2</td> +<td class="tdc br">6.5</td> +<td class="tdr"><a href="#1j">1</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4379.2</td> +<td class="tdc br">\(1^6D-^6F\)</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">3.0</td> +<td class="tdc">2.5</td> +<td class="tdc">3.0</td> +<td class="tdc">3.7</td> +<td class="tdc">2.5</td> +<td class="tdc">2.8</td> +<td class="tdc">3.5</td> +<td class="tdc">3.0</td> +<td class="tdc">4.0</td> +<td class="tdc br">4.2</td> +<td class="tdr"><a href="#2j">2</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4332.8</td> +<td class="tdc br">\(1^4G-^4G_x\)</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">4.0</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">4.5</td> +<td class="tdc">5.0</td> +<td class="tdc">4.5</td> +<td class="tdc">5.0</td> +<td class="tdc">4.0</td> +<td class="tdc">5.0</td> +<td class="tdc br">4.2</td> +<td class="tdr"><a href="#3j">3</a></td> +</tr><tr> +<td class="tdl bb br"></td> +<td class="tdc bb br">4330.1</td> +<td class="tdc bb br">\(1^4G-^4G_x\)</td> +<td class="tdc bb">0.0</td> +<td class="tdc bb">0.0</td> +<td class="tdc bb">0.0</td> +<td class="tdc bb">0.0</td> +<td class="tdc bb">0.0</td> +<td class="tdc bb">0.0</td> +<td class="tdc bb">0.0</td> +<td class="tdc bb">0.0</td> +<td class="tdc bb">4.5</td> +<td class="tdc bb">5.0</td> +<td class="tdc bb">4.5</td> +<td class="tdc bb">4.5</td> +<td class="tdc bb">4.0</td> +<td class="tdc bb">3.5</td> +<td class="tdc bb br">3.8</td> +<td class="tdr bb"><a href="#4j">4</a></td> +</tr><tr> +<td class="tdl br">Cr</td> +<td class="tdc br">4359.8</td> +<td class="tdc br">\(1^5D-1^5F\)</td> +<td class="tdc">0.0</td> +<td class="tdc">2.0</td> +<td class="tdc">..</td> +<td class="tdc">3.0</td> +<td class="tdc">..</td> +<td class="tdc">3.6</td> +<td class="tdc">5.6</td> +<td class="tdc">5.0</td> +<td class="tdc">6.8</td> +<td class="tdc">6.2</td> +<td class="tdc">6.3</td> +<td class="tdc">6.8</td> +<td class="tdc">7.1</td> +<td class="tdc">6.0</td> +<td class="tdc br">6.6</td> +<td class="tdr"><a href="#1k">1</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4351.9</td> +<td class="tdc br">\(1^5D-1^5F\)</td> +<td class="tdc">0.0</td> +<td class="tdc">2.0</td> +<td class="tdc">4.0</td> +<td class="tdc">5.0</td> +<td class="tdc">4.3</td> +<td class="tdc">6.3</td> +<td class="tdc">7.4</td> +<td class="tdc">5.0</td> +<td class="tdc">7.3</td> +<td class="tdc">8.1</td> +<td class="tdc">8.0</td> +<td class="tdc">7.0</td> +<td class="tdc">8.1</td> +<td class="tdc">8.0</td> +<td class="tdc br">9.0</td> +<td class="tdr"><a href="#2k">2</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4289.7</td> +<td class="tdc br">\(1^7S-1^7P\)</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">3.0</td> +<td class="tdc">4.4</td> +<td class="tdc">4.6</td> +<td class="tdc">7.6</td> +<td class="tdc">7.8</td> +<td class="tdc">6.7</td> +<td class="tdc">8.2</td> +<td class="tdc">7.4</td> +<td class="tdc">7.7</td> +<td class="tdc">8.6</td> +<td class="tdc">9.3</td> +<td class="tdc">11.4</td> +<td class="tdc br">10.5</td> +<td class="tdr"><a href="#3k">3</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4274.9</td> +<td class="tdc br">\(1^7S-1^7P\)</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">1.0</td> +<td class="tdc">3.0</td> +<td class="tdc">..</td> +<td class="tdc">3.5</td> +<td class="tdc">5.2</td> +<td class="tdc">5.0</td> +<td class="tdc">6.2</td> +<td class="tdc">7.2</td> +<td class="tdc">7.6</td> +<td class="tdc">9.0</td> +<td class="tdc">8.4</td> +<td class="tdc">9.5</td> +<td class="tdc br">9.4</td> +<td class="tdr"><a href="#4k">4</a></td> +</tr><tr> +<td class="tdl bb br"></td> +<td class="tdc bb br">4254.4</td> +<td class="tdc bb br">\(1^7S-1^7P\)</td> +<td class="tdc bb bb">0.0</td> +<td class="tdc bb bb">0.0</td> +<td class="tdc bb bb">0.0</td> +<td class="tdc bb">2.5</td> +<td class="tdc bb">4.0</td> +<td class="tdc bb">3.3</td> +<td class="tdc bb">4.6</td> +<td class="tdc bb">5.0</td> +<td class="tdc bb">6.4</td> +<td class="tdc bb">8.0</td> +<td class="tdc bb">8.0</td> +<td class="tdc bb">8.6</td> +<td class="tdc bb">8.6</td> +<td class="tdc bb">9.5</td> +<td class="tdc bb br">9.9</td> +<td class="tdr bb"><a href="#5k">5</a></td> +</tr><tr> +<td class="tdl br">Mn</td> +<td class="tdc br">4451.6</td> +<td class="tdc br">\(1^4D-^4D\)</td> +<td class="tdc">0.0</td> +<td class="tdc">2.0</td> +<td class="tdc">3.0</td> +<td class="tdc">..</td> +<td class="tdc">3.0</td> +<td class="tdc">2.0</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">6.0</td> +<td class="tdc">4.0</td> +<td class="tdc">3.5</td> +<td class="tdc">5.0</td> +<td class="tdc">..</td> +<td class="tdc">5.0</td> +<td class="tdc br">5.0</td> +<td class="tdr"><a href="#1l">1</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4414.9</td> +<td class="tdc br">\(1^4D-^4D\)</td> +<td class="tdc">3.0</td> +<td class="tdc">2.3</td> +<td class="tdc">3.3</td> +<td class="tdc">4.8</td> +<td class="tdc">4.6</td> +<td class="tdc">6.4</td> +<td class="tdc">8.0</td> +<td class="tdc">7.2</td> +<td class="tdc">7.0</td> +<td class="tdc">6.5</td> +<td class="tdc">7.2</td> +<td class="tdc">7.6</td> +<td class="tdc">7.4</td> +<td class="tdc">7.0</td> +<td class="tdc br">8.0</td> +<td class="tdr"><a href="#2l">2</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4041.4</td> +<td class="tdc br">\(1^6D-^6D_x\)</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">2.5</td> +<td class="tdc">2.0</td> +<td class="tdc">1.9</td> +<td class="tdc">5.2</td> +<td class="tdc">3.5</td> +<td class="tdc">6.0</td> +<td class="tdc">4.8</td> +<td class="tdc">4.8</td> +<td class="tdc">5.5</td> +<td class="tdc">6.0</td> +<td class="tdc">6.0</td> +<td class="tdc br">6.0</td> +<td class="tdr"><a href="#3l">3</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4036.5</td> +<td class="tdc br">\(1^6S-1^6P\)</td> +<td class="tdc">0.0</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">3.3</td> +<td class="tdc">4.0</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc br">..</td> +<td class="tdr"><a href="#4l">4</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4034.5</td> +<td class="tdc br">\(1^6S-1^6P\)</td> +<td class="tdc">0.0</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">5.0</td> +<td class="tdc">3.6</td> +<td class="tdc">4.0</td> +<td class="tdc">..</td> +<td class="tdc">6.0</td> +<td class="tdc">..</td> +<td class="tdc br">..</td> +<td class="tdr"><a href="#5l">5</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4033.1</td> +<td class="tdc br">\(1^6S-1^6P\)</td> +<td class="tdc">0.0</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">5.0</td> +<td class="tdc">6.0</td> +<td class="tdc">6.0</td> +<td class="tdc">4.3</td> +<td class="tdc">5.0</td> +<td class="tdc">..</td> +<td class="tdc">7.0</td> +<td class="tdc">..</td> +<td class="tdc br">..</td> +<td class="tdr"><a href="#6l">6</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4030.8</td> +<td class="tdc br">\(1^6S-1^6P\)</td> +<td class="tdc">0.0</td> +<td class="tdc">2.0</td> +<td class="tdc">1.0</td> +<td class="tdc">3.6</td> +<td class="tdc">4.0</td> +<td class="tdc">4.0</td> +<td class="tdc">5.7</td> +<td class="tdc">5.5</td> +<td class="tdc">7.0</td> +<td class="tdc">5.4</td> +<td class="tdc">6.4</td> +<td class="tdc">7.0</td> +<td class="tdc">8.0</td> +<td class="tdc">8.5</td> +<td class="tdc br">8.0</td> +<td class="tdr"><a href="#7l">7</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4068</td> +<td class="tdc br">unclas.</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">4.3</td> +<td class="tdc">..</td> +<td class="tdc">4.3</td> +<td class="tdc">7.6</td> +<td class="tdc">5.0</td> +<td class="tdc">6.6</td> +<td class="tdc">5.7</td> +<td class="tdc">5.8</td> +<td class="tdc">8.0</td> +<td class="tdc">8.5</td> +<td class="tdc">6.0</td> +<td class="tdc br">5.5</td> +<td class="tdr"><a href="#8l">8</a></td> +</tr><tr> +<td class="tdl bb br"></td> +<td class="tdc bb br">4092</td> +<td class="tdc bb br">unclas.</td> +<td class="tdc bb">..</td> +<td class="tdc bb">..</td> +<td class="tdc bb">..</td> +<td class="tdc bb">3.0</td> +<td class="tdc bb">..</td> +<td class="tdc bb">..</td> +<td class="tdc bb">..</td> +<td class="tdc bb">3.0</td> +<td class="tdc bb">4.0</td> +<td class="tdc bb">4.2</td> +<td class="tdc bb">4.2</td> +<td class="tdc bb">5.0</td> +<td class="tdc bb">5.0</td> +<td class="tdc bb">6.0</td> +<td class="tdc bb br">5.5</td> +<td class="tdr bb"><a href="#9l">9</a><span class="pagenum" id="Page_125">[Pg 125]</span></td> +</tr><tr> +<td class="tdl br">Fe</td> +<td class="tdc br">4489.7</td> +<td class="tdc br">\(1^5D-1^7F\)</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">2.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">4.2</td> +<td class="tdc">7.2</td> +<td class="tdc">6.3</td> +<td class="tdc">6.8</td> +<td class="tdc">6.8</td> +<td class="tdc">7.6</td> +<td class="tdc">8.4</td> +<td class="tdc">7.4</td> +<td class="tdc">8.0</td> +<td class="tdc br">7.6</td> +<td class="tdr"><a href="#1m">1</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4482.3</td> +<td class="tdc br">\(1^5D-1^7F\)</td> +<td class="tdc">0.0</td> +<td class="tdc">4.0</td> +<td class="tdc">4.6</td> +<td class="tdc">6.0</td> +<td class="tdc">5.5</td> +<td class="tdc">6.7</td> +<td class="tdc">8.0</td> +<td class="tdc">7.2</td> +<td class="tdc">8.1</td> +<td class="tdc">8.3</td> +<td class="tdc">8.6</td> +<td class="tdc">9.0</td> +<td class="tdc">7.7</td> +<td class="tdc">8.0</td> +<td class="tdc br">7.6</td> +<td class="tdr"><a href="#2m">2</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4461.7</td> +<td class="tdc br">\(1^5D-1^7F\)</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">3.0</td> +<td class="tdc">2.0</td> +<td class="tdc">4.2</td> +<td class="tdc">5.0</td> +<td class="tdc">6.0</td> +<td class="tdc">6.0</td> +<td class="tdc">6.0</td> +<td class="tdc">6.3</td> +<td class="tdc">6.5</td> +<td class="tdc">7.0</td> +<td class="tdc br">7.0</td> +<td class="tdr"><a href="#3m">3</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4375.9</td> +<td class="tdc br">\(1^5D-1^7F\)</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">2.5</td> +<td class="tdc">4.4</td> +<td class="tdc">5.5</td> +<td class="tdc">6.7</td> +<td class="tdc">7.1</td> +<td class="tdc">..</td> +<td class="tdc">7.8</td> +<td class="tdc">6.7</td> +<td class="tdc">6.9</td> +<td class="tdc">..</td> +<td class="tdc">8.0</td> +<td class="tdc">7.0</td> +<td class="tdc br">8.8</td> +<td class="tdr"><a href="#4m">4</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4216.1</td> +<td class="tdc br">\(1^5D-1^7P\)</td> +<td class="tdc">0.0</td> +<td class="tdc">2.0</td> +<td class="tdc">1.5</td> +<td class="tdc">3.8</td> +<td class="tdc">3.3</td> +<td class="tdc">5.6</td> +<td class="tdc">6.6</td> +<td class="tdc">2.6</td> +<td class="tdc">8.6</td> +<td class="tdc">7.3</td> +<td class="tdc">8.5</td> +<td class="tdc">9.4</td> +<td class="tdc">8.1</td> +<td class="tdc">8.0</td> +<td class="tdc br">7.9</td> +<td class="tdr"><a href="#5m">5</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4415.1</td> +<td class="tdc br">\(1^3F-^3D\)</td> +<td class="tdc">3.0</td> +<td class="tdc">2.3</td> +<td class="tdc">3.3</td> +<td class="tdc">4.8</td> +<td class="tdc">4.6</td> +<td class="tdc">6.4</td> +<td class="tdc">8.0</td> +<td class="tdc">7.2</td> +<td class="tdc">7.0</td> +<td class="tdc">6.5</td> +<td class="tdc">7.2</td> +<td class="tdc">7.6</td> +<td class="tdc">7.4</td> +<td class="tdc">7.0</td> +<td class="tdc br">8.0</td> +<td class="tdr"><a href="#6m">6</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4404.7</td> +<td class="tdc br">\(1^3F-^3D\)</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">6.0</td> +<td class="tdc">4.4</td> +<td class="tdc">6.7</td> +<td class="tdc">5.0</td> +<td class="tdc">6.1</td> +<td class="tdc">7.4</td> +<td class="tdc">7.8</td> +<td class="tdc">8.8</td> +<td class="tdc">8.0</td> +<td class="tdc">8.0</td> +<td class="tdc br">9.1</td> +<td class="tdr"><a href="#7m">7</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">43834</td> +<td class="tdc br">\(1^3F-^3D\)</td> +<td class="tdc">3.0</td> +<td class="tdc">2.5</td> +<td class="tdc">4.0</td> +<td class="tdc">5.4</td> +<td class="tdc">4.6</td> +<td class="tdc">6.7</td> +<td class="tdc">7.0</td> +<td class="tdc">8.2</td> +<td class="tdc">9.1</td> +<td class="tdc">10.3</td> +<td class="tdc">10.3</td> +<td class="tdc">10.5</td> +<td class="tdc">9.9</td> +<td class="tdc">11.0</td> +<td class="tdc br">10.3</td> +<td class="tdr"><a href="#8m">8</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4337.0</td> +<td class="tdc br">\(1^3F-^3D\)</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">5.0</td> +<td class="tdc">6.3</td> +<td class="tdc">5.0</td> +<td class="tdc">7.2</td> +<td class="tdc">7.8</td> +<td class="tdc">7.2</td> +<td class="tdc">7.2</td> +<td class="tdc">8.9</td> +<td class="tdc">9.0</td> +<td class="tdc br">8.3</td> +<td class="tdr"><a href="#9m">9</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4291.4</td> +<td class="tdc br">\(1^3F-^3D\)</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">3.0</td> +<td class="tdc">4.4</td> +<td class="tdc">4.6</td> +<td class="tdc">7.6</td> +<td class="tdc">7.8</td> +<td class="tdc">6.7</td> +<td class="tdc">8.2</td> +<td class="tdc">7.4</td> +<td class="tdc">7.7</td> +<td class="tdc">8.6</td> +<td class="tdc">9.3</td> +<td class="tdc">11.0</td> +<td class="tdc br">10.5</td> +<td class="tdr"><a href="#10m">10</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4325.8</td> +<td class="tdc br">\(1^3F-^3G\)</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">3.5</td> +<td class="tdc">5.5</td> +<td class="tdc">3.3</td> +<td class="tdc">6.3</td> +<td class="tdc">7.8</td> +<td class="tdc">9.0</td> +<td class="tdc">10.0</td> +<td class="tdc">11.0</td> +<td class="tdc">11.3</td> +<td class="tdc">11.7</td> +<td class="tdc">10.9</td> +<td class="tdc">11.0</td> +<td class="tdc br">10.2</td> +<td class="tdr"><a href="#11m">11</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4307.9</td> +<td class="tdc br">\(1^3F-^3G\)</td> +<td class="tdc">0.0</td> +<td class="tdc">3.3</td> +<td class="tdc">3.0</td> +<td class="tdc">4.0</td> +<td class="tdc">3.6</td> +<td class="tdc">4.9</td> +<td class="tdc">6.5</td> +<td class="tdc">7.2</td> +<td class="tdc">9.5</td> +<td class="tdc">8.6</td> +<td class="tdc">8.6</td> +<td class="tdc">10.3</td> +<td class="tdc">10.5</td> +<td class="tdc">12.0</td> +<td class="tdc br">13.1</td> +<td class="tdr"><a href="#12m">12</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4271.8</td> +<td class="tdc br">\(1^3F-^3G\)</td> +<td class="tdc">0.0</td> +<td class="tdc">2.3</td> +<td class="tdc">2.5</td> +<td class="tdc">4.2</td> +<td class="tdc">4.5</td> +<td class="tdc">4.5</td> +<td class="tdc">6.5</td> +<td class="tdc">6.3</td> +<td class="tdc">7.2</td> +<td class="tdc">8.3</td> +<td class="tdc">8.6</td> +<td class="tdc">9.2</td> +<td class="tdc">8.7</td> +<td class="tdc">10.0</td> +<td class="tdc br">9.1</td> +<td class="tdr"><a href="#13m">13</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4260.5</td> +<td class="tdc br">\(1^3F-^3G\)</td> +<td class="tdc">0.0</td> +<td class="tdc">3.0</td> +<td class="tdc">1.5</td> +<td class="tdc">4.2</td> +<td class="tdc">4.0</td> +<td class="tdc">..</td> +<td class="tdc">5.5</td> +<td class="tdc">6.6</td> +<td class="tdc">7.0</td> +<td class="tdc">8.0</td> +<td class="tdc">8.8</td> +<td class="tdc">9.0</td> +<td class="tdc">8.1</td> +<td class="tdc">10.0</td> +<td class="tdc br">9.0</td> +<td class="tdr"><a href="#14m">14</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4290.8</td> +<td class="tdc br">\(1^3F-^3G\)</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">2.0</td> +<td class="tdc">3.6</td> +<td class="tdc">4.0</td> +<td class="tdc">5.6</td> +<td class="tdc">5.3</td> +<td class="tdc">6.3</td> +<td class="tdc">6.4</td> +<td class="tdc">7.8</td> +<td class="tdc">7.9</td> +<td class="tdc">8.4</td> +<td class="tdc">8.0</td> +<td class="tdc">9.0</td> +<td class="tdc br">7.6</td> +<td class="tdr"><a href="#15m">15</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4143.9</td> +<td class="tdc br">\(1^3F-^3F\)</td> +<td class="tdc">0.0</td> +<td class="tdc">2.0</td> +<td class="tdc">2.5</td> +<td class="tdc">4.4</td> +<td class="tdc">3.3</td> +<td class="tdc">4.8</td> +<td class="tdc">6.1</td> +<td class="tdc">5.7</td> +<td class="tdc">7.7</td> +<td class="tdc">7.7</td> +<td class="tdc">8.9</td> +<td class="tdc">8.6</td> +<td class="tdc">8.5</td> +<td class="tdc">11.0</td> +<td class="tdc br">10.0</td> +<td class="tdr"><a href="#16m">16</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4132.</td> +<td class="tdc br">\(1^3F-^3F\)</td> +<td class="tdc">0.0</td> +<td class="tdc">3.6</td> +<td class="tdc">2.0</td> +<td class="tdc">4.0</td> +<td class="tdc">2.0</td> +<td class="tdc">4.2</td> +<td class="tdc">6.0</td> +<td class="tdc">4.0</td> +<td class="tdc">6.0</td> +<td class="tdc">5.2</td> +<td class="tdc">5.5</td> +<td class="tdc">6.0</td> +<td class="tdc">6.5</td> +<td class="tdc">5.0</td> +<td class="tdc br">4.0</td> +<td class="tdr"><a href="#17m">17</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4071.7</td> +<td class="tdc br">\(1^3F-^3F\)</td> +<td class="tdc">0.0</td> +<td class="tdc">2.0</td> +<td class="tdc">2.0</td> +<td class="tdc">4.0</td> +<td class="tdc">3.0</td> +<td class="tdc">4.3</td> +<td class="tdc">6.6</td> +<td class="tdc">5.7</td> +<td class="tdc">7.8</td> +<td class="tdc">7.5</td> +<td class="tdc">9.2</td> +<td class="tdc">9.0</td> +<td class="tdc">9.0</td> +<td class="tdc">9.5</td> +<td class="tdc br">8.6</td> +<td class="tdr"><a href="#18m">18</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4063.6</td> +<td class="tdc br">\(1^3F-^3F\)</td> +<td class="tdc">0.0</td> +<td class="tdc">2.0</td> +<td class="tdc">2.0</td> +<td class="tdc">3.6</td> +<td class="tdc">4.0</td> +<td class="tdc">4.8</td> +<td class="tdc">5.8</td> +<td class="tdc">5.6</td> +<td class="tdc">7.2</td> +<td class="tdc">7.5</td> +<td class="tdc">8.0</td> +<td class="tdc">9.0</td> +<td class="tdc">8.0</td> +<td class="tdc">9.5</td> +<td class="tdc br">9.0</td> +<td class="tdr"><a href="#19m">19</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4045.8</td> +<td class="tdc br">\(1^3F-^3F\)</td> +<td class="tdc">0.0</td> +<td class="tdc">2.0</td> +<td class="tdc">2.5</td> +<td class="tdc">4.6</td> +<td class="tdc">5.0</td> +<td class="tdc">5.6</td> +<td class="tdc">6.9</td> +<td class="tdc">7.6</td> +<td class="tdc">8.8</td> +<td class="tdc">9.2</td> +<td class="tdc">10.3</td> +<td class="tdc">10.6</td> +<td class="tdc">8.6</td> +<td class="tdc">11.0</td> +<td class="tdc br">10.8</td> +<td class="tdr"><a href="#20m">20</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4005.2</td> +<td class="tdc br">\(1^3F-^3F\)</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">2.5</td> +<td class="tdc">4.6</td> +<td class="tdc">5.5</td> +<td class="tdc">5.0</td> +<td class="tdc">6.3</td> +<td class="tdc">6.0</td> +<td class="tdc">8.3</td> +<td class="tdc">7.2</td> +<td class="tdc">6.6</td> +<td class="tdc">9.0</td> +<td class="tdc">8.0</td> +<td class="tdc">7.0</td> +<td class="tdc br">..</td> +<td class="tdr"><a href="#21m">21</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4299.2</td> +<td class="tdc br">\(1^7D-^7D\)</td> +<td class="tdc">0.0</td> +<td class="tdc">3.0</td> +<td class="tdc">3.0</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">6.0</td> +<td class="tdc">7.6</td> +<td class="tdc">7.0</td> +<td class="tdc">5.0</td> +<td class="tdc">6.5</td> +<td class="tdc">5.0</td> +<td class="tdc">8.0</td> +<td class="tdc">5.6</td> +<td class="tdc">10.3</td> +<td class="tdc br">13.0</td> +<td class="tdr"><a href="#22m">22</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4271.2</td> +<td class="tdc br">\(1^7D-^7D\)</td> +<td class="tdc">0.0</td> +<td class="tdc">2.3</td> +<td class="tdc">2.5</td> +<td class="tdc">4.2</td> +<td class="tdc">4.5</td> +<td class="tdc">4.2</td> +<td class="tdc">6.5</td> +<td class="tdc">6.3</td> +<td class="tdc">7.2</td> +<td class="tdc">8.3</td> +<td class="tdc">8.6</td> +<td class="tdc">9.2</td> +<td class="tdc">8.7</td> +<td class="tdc">10.0</td> +<td class="tdc br">9.1</td> +<td class="tdr"><a href="#23m">23</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4260.5</td> +<td class="tdc br">\(1^7D-^7D\)</td> +<td class="tdc">0.0</td> +<td class="tdc">3.0</td> +<td class="tdc">1.5</td> +<td class="tdc">4.2</td> +<td class="tdc">4.0</td> +<td class="tdc">..</td> +<td class="tdc">5.5</td> +<td class="tdc">6.6</td> +<td class="tdc">7.0</td> +<td class="tdc">8.0</td> +<td class="tdc">8.0</td> +<td class="tdc">9.0</td> +<td class="tdc">8.1</td> +<td class="tdc">8.5</td> +<td class="tdc br">9.0</td> +<td class="tdr"><a href="#24m">24</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4250.1</td> +<td class="tdc br">\(1^7D-^7D\)</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">2.0</td> +<td class="tdc">3.6</td> +<td class="tdc">4.0</td> +<td class="tdc">5.6</td> +<td class="tdc">5.3</td> +<td class="tdc">6.3</td> +<td class="tdc">6.4</td> +<td class="tdc">7.8</td> +<td class="tdc">7.9</td> +<td class="tdc">8.4</td> +<td class="tdc">8.0</td> +<td class="tdc">9.0</td> +<td class="tdc br">7.6</td> +<td class="tdr"><a href="#25m">25</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4187.8</td> +<td class="tdc br">\(1^7D-^7D\)</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">2.0</td> +<td class="tdc">5.0</td> +<td class="tdc">6.0</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">6.0</td> +<td class="tdc">5.5</td> +<td class="tdc">6.0</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc br">8.0</td> +<td class="tdr"><a href="#26m">26</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4482.3</td> +<td class="tdc br">\(1^5P-3^5D'\)</td> +<td class="tdc">0.0</td> +<td class="tdc">4.0</td> +<td class="tdc">4.6</td> +<td class="tdc">6.0</td> +<td class="tdc">5.5</td> +<td class="tdc">6.7</td> +<td class="tdc">8.0</td> +<td class="tdc">7.2</td> +<td class="tdc">8.1</td> +<td class="tdc">8.3</td> +<td class="tdc">8.6</td> +<td class="tdc">9.0</td> +<td class="tdc">7.7</td> +<td class="tdc">8.0</td> +<td class="tdc br">7.6</td> +<td class="tdr"><a href="#27m">27</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4408.4</td> +<td class="tdc br">\(1^5P-3^5D'\)</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">4.0</td> +<td class="tdc">3.5</td> +<td class="tdc">5.7</td> +<td class="tdc">4.0</td> +<td class="tdc">5.6</td> +<td class="tdc">6.0</td> +<td class="tdc">6.0</td> +<td class="tdc">8.0</td> +<td class="tdc">7.9</td> +<td class="tdc">7.0</td> +<td class="tdc br">9.0</td> +<td class="tdr"><a href="#28m">28</a><span class="pagenum" id="Page_126">[Pg 126]</span></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4352.7</td> +<td class="tdc br">\(1^5P-1^5S'\)</td> +<td class="tdc">0.0</td> +<td class="tdc">2.0</td> +<td class="tdc">4.0</td> +<td class="tdc">5.0</td> +<td class="tdc">4.3</td> +<td class="tdc">6.3</td> +<td class="tdc">7.4</td> +<td class="tdc">5.0</td> +<td class="tdc">7.3</td> +<td class="tdc">8.1</td> +<td class="tdc">8.0</td> +<td class="tdc">7.0</td> +<td class="tdc">8.1</td> +<td class="tdc">8.0</td> +<td class="tdc br">9.0</td> +<td class="tdr"><a href="#29m">29</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4315-1</td> +<td class="tdc br">\(1^5P-1^5S'\)</td> +<td class="tdc">0.0</td> +<td class="tdc">3.0</td> +<td class="tdc">3.5</td> +<td class="tdc">5.0</td> +<td class="tdc">4.6</td> +<td class="tdc">6.9</td> +<td class="tdc">7.5</td> +<td class="tdc">4.6</td> +<td class="tdc">6.6</td> +<td class="tdc">5.6</td> +<td class="tdc">6.1</td> +<td class="tdc">7.0</td> +<td class="tdc">7.0</td> +<td class="tdc">8.0</td> +<td class="tdc br">8.1</td> +<td class="tdr"><a href="#30m">30</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4282.4</td> +<td class="tdc br">\(1^5P-1^5S'\)</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">5.0</td> +<td class="tdc">3.0</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">4.0</td> +<td class="tdc">5.0</td> +<td class="tdc">6.1</td> +<td class="tdc">5.0</td> +<td class="tdc">6.0</td> +<td class="tdc">8.0</td> +<td class="tdc br">4.4</td> +<td class="tdr"><a href="#31m">31</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4258.4</td> +<td class="tdc br">\(1^5P-1^5P'\)</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">4.0</td> +<td class="tdc">4.8</td> +<td class="tdc">..</td> +<td class="tdc">4.5</td> +<td class="tdc">5.2</td> +<td class="tdc">4.3</td> +<td class="tdc">4.5</td> +<td class="tdc">5.3</td> +<td class="tdc">10.0</td> +<td class="tdc br">4.0</td> +<td class="tdr"><a href="#32m">32</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4216.2</td> +<td class="tdc br">\(1^5P-1^5P'\)</td> +<td class="tdc">0.0</td> +<td class="tdc">2.0</td> +<td class="tdc">1.5</td> +<td class="tdc">3.8</td> +<td class="tdc">3.3</td> +<td class="tdc">5.6</td> +<td class="tdc">6.6</td> +<td class="tdc">2.6</td> +<td class="tdc">8.6</td> +<td class="tdc">7.3</td> +<td class="tdc">8.5</td> +<td class="tdc">9.4</td> +<td class="tdc">8.1</td> +<td class="tdc">9.5</td> +<td class="tdc br">7.9</td> +<td class="tdr"><a href="#33m">33</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4134.3</td> +<td class="tdc br">\(1^5P-1^5P'\)</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">3.0</td> +<td class="tdc">2.0</td> +<td class="tdc">4.0</td> +<td class="tdc">3.5</td> +<td class="tdc">4.5</td> +<td class="tdc">5.5</td> +<td class="tdc">5.2</td> +<td class="tdc">5.6</td> +<td class="tdc">7.0</td> +<td class="tdc">7.0</td> +<td class="tdc">5.0</td> +<td class="tdc br">5.5</td> +<td class="tdr"><a href="#34m">34</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">3953</td> +<td class="tdc br">unclas.</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">2.0</td> +<td class="tdc">5.3</td> +<td class="tdc">..</td> +<td class="tdc">5.7</td> +<td class="tdc">5.5</td> +<td class="tdc">..</td> +<td class="tdc">8.0</td> +<td class="tdc">8.0</td> +<td class="tdc">7.5</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc br">..</td> +<td class="tdr"><a href="#35m">35</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">3999</td> +<td class="tdc br">unclas.</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">1.5</td> +<td class="tdc">4.5</td> +<td class="tdc">6.0</td> +<td class="tdc">5.6</td> +<td class="tdc">7.0</td> +<td class="tdc">6.0</td> +<td class="tdc">7.6</td> +<td class="tdc">7.0</td> +<td class="tdc">6.5</td> +<td class="tdc">..</td> +<td class="tdc">7.0</td> +<td class="tdc">8.0</td> +<td class="tdc br">..</td> +<td class="tdr"><a href="#36m">36</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4172</td> +<td class="tdc br">unclas.</td> +<td class="tdc">0.0</td> +<td class="tdc">2.0</td> +<td class="tdc">3.0</td> +<td class="tdc">4.6</td> +<td class="tdc">4.6</td> +<td class="tdc">6.3</td> +<td class="tdc">9.0</td> +<td class="tdc">5.7</td> +<td class="tdc">7.3</td> +<td class="tdc">5.8</td> +<td class="tdc">6.4</td> +<td class="tdc">7.3</td> +<td class="tdc">6.0</td> +<td class="tdc">9.0</td> +<td class="tdc br">8.2</td> +<td class="tdr"><a href="#37m">37</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4401</td> +<td class="tdc br">unclas.</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">3.0</td> +<td class="tdc">6.0</td> +<td class="tdc">6.6</td> +<td class="tdc">8.0</td> +<td class="tdc">6.2</td> +<td class="tdc">6.8</td> +<td class="tdc">6.0</td> +<td class="tdc">5.5</td> +<td class="tdc">6.2</td> +<td class="tdc">6.9</td> +<td class="tdc">6.0</td> +<td class="tdc br">6.5</td> +<td class="tdr"><a href="#38m">38</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4462</td> +<td class="tdc br">unclas.</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">3.0</td> +<td class="tdc">2.0</td> +<td class="tdc">4.2</td> +<td class="tdc">5.0</td> +<td class="tdc">6.0</td> +<td class="tdc">6.0</td> +<td class="tdc">6.0</td> +<td class="tdc">6.3</td> +<td class="tdc">6.5</td> +<td class="tdc">7.2</td> +<td class="tdc br">7.0</td> +<td class="tdr"><a href="#39m">39</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4476</td> +<td class="tdc br">unclas.</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">3.0</td> +<td class="tdc">5.0</td> +<td class="tdc">5.2</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">6.3</td> +<td class="tdc">4.0</td> +<td class="tdc">4.1</td> +<td class="tdc">4.0</td> +<td class="tdc">4.3</td> +<td class="tdc">7.5</td> +<td class="tdc br">4.7</td> +<td class="tdr"><a href="#40m">40</a></td> +</tr><tr> +<td class="tdl br">Fe+</td> +<td class="tdc br">4173.3</td> +<td class="tdc br">\(2^4P-1^4D'\)</td> +<td class="tdc">0.0</td> +<td class="tdc">2.0</td> +<td class="tdc">3.0</td> +<td class="tdc">4.6</td> +<td class="tdc">4.6</td> +<td class="tdc">6.3</td> +<td class="tdc">9.0</td> +<td class="tdc">5.7</td> +<td class="tdc">7.3</td> +<td class="tdc">5.8</td> +<td class="tdc">6.4</td> +<td class="tdc">7.3</td> +<td class="tdc">6.0</td> +<td class="tdc">8.0</td> +<td class="tdc br">8.2</td> +<td class="tdr"><a href="#41m">41</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4178.8</td> +<td class="tdc br">\(2^4P-1^4F\)</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">2.5</td> +<td class="tdc">4.3</td> +<td class="tdc">..</td> +<td class="tdc">6.8</td> +<td class="tdc">9.1</td> +<td class="tdc">..</td> +<td class="tdc">6.0</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc br">6.5</td> +<td class="tdr"><a href="#42m">42</a></td> +</tr><tr> +<td class="tdl bb br"></td> +<td class="tdc bb br">4416.8</td> +<td class="tdc bb br">\(2^4P-1^4D'\)</td> +<td class="tdc bb">0.0</td> +<td class="tdc bb">2.3</td> +<td class="tdc bb">3.3</td> +<td class="tdc bb">4.8</td> +<td class="tdc bb">4.6</td> +<td class="tdc bb">6.4</td> +<td class="tdc bb">8.0</td> +<td class="tdc bb">7.2</td> +<td class="tdc bb">7.0</td> +<td class="tdc bb">6.5</td> +<td class="tdc bb">7.2</td> +<td class="tdc bb">7.6</td> +<td class="tdc bb">7.4</td> +<td class="tdc bb">7.0</td> +<td class="tdc bb br">8.0</td> +<td class="tdr bb"><a href="#43m">43</a></td> +</tr><tr> +<td class="tdl br">Zn</td> +<td class="tdc br">4810.5</td> +<td class="tdc br">\(1^3P-1^3S\)</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">tr</td> +<td class="tdc">..</td> +<td class="tdc">tr</td> +<td class="tdc">1</td> +<td class="tdc">tr</td> +<td class="tdc">0</td> +<td class="tdc">..</td> +<td class="tdc">0</td> +<td class="tdc">..</td> +<td class="tdc br">..</td> +<td class="tdr"><a href="#1n">1</a></td> +</tr><tr> +<td class="tdl bb br"></td> +<td class="tdc bb br">4722.2</td> +<td class="tdc bb br">\(1^3P-1^3S\)</td> +<td class="tdc bb">0.0</td> +<td class="tdc bb">0.0</td> +<td class="tdc bb">0.0</td> +<td class="tdc bb">0.0</td> +<td class="tdc bb">tr</td> +<td class="tdc bb">tr</td> +<td class="tdc bb">..</td> +<td class="tdc bb">tr</td> +<td class="tdc bb">1</td> +<td class="tdc bb">tr</td> +<td class="tdc bb">1-</td> +<td class="tdc bb">..</td> +<td class="tdc bb">1-</td> +<td class="tdc bb">..</td> +<td class="tdc bb br">..</td> +<td class="tdr bb"><a href="#2n">2</a></td> +</tr><tr> +<td class="tdl br">Sr</td> +<td class="tdc br">4607.3</td> +<td class="tdc br">\(_1S-_1P\)</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">2.0</td> +<td class="tdc">4.0</td> +<td class="tdc">..</td> +<td class="tdc">7.0</td> +<td class="tdc">..</td> +<td class="tdc">8.5</td> +<td class="tdc">8.0</td> +<td class="tdc">8.7</td> +<td class="tdc">9.0</td> +<td class="tdc br">9.2</td> +<td class="tdr"><a href="#1o">1</a></td> +</tr><tr> +<td class="tdl br">Sr+</td> +<td class="tdc br">4215.5</td> +<td class="tdc br">\(1^2S-1^2P\)</td> +<td class="tdc">..</td> +<td class="tdc">2.0</td> +<td class="tdc">1.5</td> +<td class="tdc">3.8</td> +<td class="tdc">3.3</td> +<td class="tdc">5.6</td> +<td class="tdc">6.6</td> +<td class="tdc">2.6</td> +<td class="tdc">8.6</td> +<td class="tdc">5.3</td> +<td class="tdc">8.5</td> +<td class="tdc">9.4</td> +<td class="tdc">8.1</td> +<td class="tdc">8.0</td> +<td class="tdc br">7.9</td> +<td class="tdr"><a href="#2o">2</a></td> +</tr><tr> +<td class="tdl bb br"></td> +<td class="tdc bb br">4077.7</td> +<td class="tdc bb br">\(1^2S-1^2P\)</td> +<td class="tdc bb">..</td> +<td class="tdc bb">4.2</td> +<td class="tdc bb">2.5</td> +<td class="tdc bb">4.2</td> +<td class="tdc bb">5.0</td> +<td class="tdc bb">6.9</td> +<td class="tdc bb">8.4</td> +<td class="tdc bb">8.6</td> +<td class="tdc bb">9.2</td> +<td class="tdc bb">7.8</td> +<td class="tdc bb">9.5</td> +<td class="tdc bb">9.3</td> +<td class="tdc bb">8.3</td> +<td class="tdc bb">11.0</td> +<td class="tdc bb br">10.8</td> +<td class="tdr bb"><a href="#3o">3</a></td> +</tr><tr> +<td class="tdl br">Y+</td> +<td class="tdc br">4374.9</td> +<td class="tdc br"></td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">2.5</td> +<td class="tdc">2.4</td> +<td class="tdc">5.5</td> +<td class="tdc">6.7</td> +<td class="tdc">7.1</td> +<td class="tdc">..</td> +<td class="tdc">7.8</td> +<td class="tdc">6.7</td> +<td class="tdc">6.9</td> +<td class="tdc">..</td> +<td class="tdc">8.0</td> +<td class="tdc">8.8</td> +<td class="tdc br">9.6</td> +<td class="tdr"><a href="#1p">1</a></td> +</tr><tr> +<td class="tdl br"></td> +<td class="tdc br">4177.5</td> +<td class="tdc br"></td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">2.5</td> +<td class="tdc">4.3</td> +<td class="tdc">..</td> +<td class="tdc">6.8</td> +<td class="tdc">9.1</td> +<td class="tdc">..</td> +<td class="tdc">6.0</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc br">6.5</td> +<td class="tdr"><a href="#2p">2</a></td> +</tr><tr> +<td class="tdl bb br"></td> +<td class="tdc bb br">4398.</td> +<td class="tdc bb br">\(^3D-^3P\)</td> +<td class="tdc bb">..</td> +<td class="tdc bb">..</td> +<td class="tdc bb">..</td> +<td class="tdc bb">..</td> +<td class="tdc bb">..</td> +<td class="tdc bb">..</td> +<td class="tdc bb">..</td> +<td class="tdc bb">..</td> +<td class="tdc bb">7.0</td> +<td class="tdc bb">..</td> +<td class="tdc bb">..</td> +<td class="tdc bb">4.0</td> +<td class="tdc bb">2.6</td> +<td class="tdc bb">2.0</td> +<td class="tdc bb br">3.7</td> +<td class="tdr bb"><a href="#3p">3</a></td> +</tr><tr> +<td class="tdl bb br">Ba+</td> +<td class="tdc bb br">4554</td> +<td class="tdc bb br">\(1^2S-1^2P1\)</td> +<td class="tdc bb">0.0</td> +<td class="tdc bb">0.0</td> +<td class="tdc bb">2.0</td> +<td class="tdc bb">..</td> +<td class="tdc bb">..</td> +<td class="tdc bb">4.0</td> +<td class="tdc bb">4.7</td> +<td class="tdc bb">..</td> +<td class="tdc bb">3.5</td> +<td class="tdc bb">3.0</td> +<td class="tdc bb">4.6</td> +<td class="tdc bb">4.8</td> +<td class="tdc bb">5.5</td> +<td class="tdc bb">5.5</td> +<td class="tdc bb br">5.6</td> +<td class="tdr bb"><a href="#1q">1</a><span class="pagenum" id="Page_127">[Pg 127]</span></td> +</tr> + </tbody> +</table> + + +<h2><a id="NOTES_ON_OBSERVATIONAL_MATERIAL">NOTES ON OBSERVATIONAL MATERIAL</a></h2> + +<p class="nindc" > +NOTES TO TABLE XIX</p> +<table class="autotable"> +<thead><tr> +<th class="tdc">Atom </th> +<th class="tdc"> Note </th> +<th class="tdl"> Max. </th> +<th class="tdc"> Blends </th> +<th class="tdc"> Remarks</th> +</tr> +</thead> +<tbody><tr> +<td class="tdl_top">H</td> +<td class="tdc_top"><a id="1a">1</a></td> +<td class="tdc_top">\(A_0\)</td> +<td class="tdc_top">..</td> +<td class="tdl">No measures available across the whole +range of these lines. They are blended with He+ in the \(O\) +types. For a discussion of the maximum of these lines, +see <a href="#Page_166">p. 166</a></td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"><a id="2a">2</a></td> +<td class="tdc">\(A_0\)</td> +<td class="tdc">..</td> +<td class="tdl"></td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"><a id="3a">3</a></td> +<td class="tdc">\(A_0\)</td> +<td class="tdc">..</td> +<td class="tdc"></td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"><a id="4a">4</a></td> +<td class="tdc">\(A_0\)</td> +<td class="tdc">..</td> +<td class="tdl"></td> +</tr><tr> +<td class="tdl_top">He</td> +<td class="tdc_top"><a id="1b">1</a>,<a id="2b">2</a>,<a id="3b">3</a>, 4 +<a id="5b">5</a>,<a id="6b">6</a>,<a id="7b">7</a>,<a id="8b">8</a></td> +<td class="tdc_top">\(B_3\)</td> +<td class="tdc_top">..</td> +<td class="tdl_top">Maximum well determined. +Unblended</td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"><a id="4b">4</a></td> +<td class="tdc">\(B_3\)</td> +<td class="tdc">He+</td> +<td class="tdl">See Note 12</td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"><a id="9b">9</a>,<a id="10b">10</a>,<a id="11b">11</a>,<a id="12b">12</a></td> +<td class="tdc">\(O\)</td> +<td class="tdc"></td> +<td class="tdl">Probably blended. See H. C. 263, 1924</td> +</tr><tr> +<td class="tdl">C</td> +<td class="tdc"><a id="1c">1</a></td> +<td class="tdc">\(B_3\)</td> +<td class="tdc">..</td> +<td class="tdl">Unblended</td> +</tr><tr> +<td class="tdl">Mg</td> +<td class="tdc"><a id="1d">1</a></td> +<td class="tdc">\(K_2\)?</td> +<td class="tdc">..</td> +<td class="tdl">Effectively unblended. Material very +meager</td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"><a id="2d">2</a></td> +<td class="tdc">\(K_5\)</td> +<td class="tdc">..</td> +<td class="tdl">Unblended</td> +</tr><tr> +<td class="tdl_top"></td> +<td class="tdc_top"><a id="3d">3</a></td> +<td class="tdc_top">none</td> +<td class="tdc">\(Fe_2\); \(Cr_5\); \(Mg_5\)</td> +<td class="tdl_top">Cr probably predominates</td> +</tr><tr> +<td class="tdl_top"></td> +<td class="tdc_top"><a id="4d">4</a></td> +<td class="tdc_top">\(A_2\)</td> +<td class="tdc_top">-, \(Fe_5\); \(Fe_3\)</td> +<td class="tdl">Fe predominates at lower temperature; Mg probably +responsible for maximum</td> +</tr><tr> +<td class="tdl">Al</td> +<td class="tdc"><a id="1e">1</a></td> +<td class="tdc">none</td> +<td class="tdc">..</td> +<td class="tdl"></td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"><a id="2e">2</a></td> +<td class="tdc">none</td> +<td class="tdc">..</td> +<td class="tdl"></td> +</tr><tr> +<td class="tdl_top">Si</td> +<td class="tdc_top"><a id="1f">1</a></td> +<td class="tdc_top">\(G_0\)</td> +<td class="tdc_top">-2; -1; \(Si_12\); -2; -1</td> +<td class="tdl">Si predominates, and is responsible +for maximum</td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"><a id="2f">2</a></td> +<td class="tdc">\(A_0\)</td> +<td class="tdc"></td> +<td class="tdl"></td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"><a id="3f">3</a><a id="4f">4</a>,<a id="5f">5</a></td> +<td class="tdc">\(B_1-B_2\)</td> +<td class="tdc">..</td> +<td class="tdl"></td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"><a id="6f">6</a></td> +<td class="tdc">\(B_0-O\)</td> +<td class="tdc">..</td> +<td class="tdl"></td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"><a id="7f">7</a></td> +<td class="tdc">\(B_0-O\)</td> +<td class="tdc">N++</td> +<td class="tdl"></td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"><a id="8f">8</a></td> +<td class="tdc">\(B_0-O\)</td> +<td class="tdc"></td> +<td class="tdl"></td> +</tr><tr> +<td class="tdl_top">Ca</td> +<td class="tdc_top"><a id="1g">1</a></td> +<td class="tdc_top">\(M_a\)</td> +<td class="tdc_top">\(Ca_4\); \(C_0\); \(Fe_4\)</td> +<td class="tdl_top">Ca probably responsible for rise at +\(M_a\)</td> +</tr><tr> +<td class="tdl_top"></td> +<td class="tdc_top"><a id="2g">2</a></td> +<td class="tdc_top">\(M_a\)</td> +<td class="tdc_top">Ca, \(Zr_5\); \(Mn_1\); Mn, +\(Ti_2\); \(Mn_2\); \(Ca_2\)</td> +<td class="tdl_top">Ca probably predominates. Enhanced +line suspected near \(G_0\)</td> +</tr><tr> +<td class="tdl_top"></td> +<td class="tdc_top"><a id="3g">3</a></td> +<td class="tdc_top">\(M_a\)</td> +<td class="tdc_top">\(Ca_5\); \(Fe_2\); \(Ca_4\)</td> +<td class="tdl">Calcium predominates. Enhanced +line suspected near \(G_0\)</td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"><a id="4g">4</a></td> +<td class="tdc">none</td> +<td class="tdc">\(Ca_3\); \(Fe_6\)</td> +<td class="tdl">In \(G\) band</td> +</tr><tr> +<td class="tdl_top"></td> +<td class="tdc_top"><a id="5g">5</a></td> +<td class="tdc_top">none</td> +<td class="tdc_top">\(Ti_2\); \(Fe_2\); -2; \(Ca_4\); +-2</td> +<td class="tdl_top">Maximum undetermined. In \(G\) +band</td> +</tr><tr> +<td class="tdl_top"></td> +<td class="tdc_top"><a id="6g">6</a></td> +<td class="tdc_top">\(K_2\)</td> +<td class="tdc_top">\(Ti_2\); -2; \(Ca_3\); -1; +Ti, Fe 4</td> +<td class="tdl_top">Fe probably responsible for maximum</td> +</tr><tr> +<td class="tdl_top"></td> +<td class="tdc_top"><a id="7g">7</a></td> +<td class="tdc_top">\(M_a\)?</td> +<td class="tdc_top">\(Ti_2\); \(Ca_4\); \(Ti_2\); +\(Cr_5\); Ti; \(Fe_1\)</td> +<td class="tdl">Chromium (ultimate) line probably +obliterates the Ca line. Maximum at \(M_a\) due to Ca?</td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"><a id="8g">8</a></td> +<td class="tdc">\(M_a\)</td> +<td class="tdc">\(Fe_5\); \(Ca_4\)</td> +<td class="tdl"></td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"><a id="9g">9</a></td> +<td class="tdc">none</td> +<td class="tdc"></td> +<td class="tdl">Unblended</td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"><a id="10g">10</a></td> +<td class="tdc">?</td> +<td class="tdc"></td> +<td class="tdl">Hydrogen predominates before \(A_3\) +<span class="pagenum" id="Page_128">[Pg 128]</span></td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"><a id="11g">11</a></td> +<td class="tdc">?</td> +<td class="tdc"></td> +<td class="tdl">Unblended</td> +</tr><tr> +<td class="tdl">Sc</td> +<td class="tdc"><a id="1h">1</a></td> +<td class="tdc">\(F_5\)</td> +<td class="tdc">Y? \(_5\); \(Fe_4\)</td> +<td class="tdl">Sc predominates, at least at maximum</td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"><a id="2h">2</a></td> +<td class="tdc">\(F_5\)</td> +<td class="tdc">\(Sc_3\); -2</td> +<td class="tdl">Sc predominates</td> +</tr><tr> +<td class="tdl">Ti</td> +<td class="tdc"><a id="1i">1</a></td> +<td class="tdc">\(K_5\)</td> +<td class="tdc">\(Ti_3\); V, \(Zr_2\)</td> +<td class="tdl">Blended with Ti+. See Note 10</td> +</tr><tr> +<td class="tdl_top"></td> +<td class="tdc_top"><a id="2i">2</a></td> +<td class="tdc_top">(none)</td> +<td class="tdc_top">\(Ti_2\); \(Fe_2\); \(Ca_4\); -2; -2</td> +<td class="tdl_top">Ca causes rise at \(M_a\). Ti obliterated</td> +</tr><tr> +<td class="tdl_top"></td> +<td class="tdc_top"><a id="3i">3</a></td> +<td class="tdc_top">\(K_2\)</td> +<td class="tdc_top">\(Ti_3\)</td> +<td class="tdl">Ti+ causes rise at \(F_5\). Rise at \(M_a\) +unexplained</td> +</tr><tr> +<td class="tdl_top"></td> +<td class="tdc_top"><a id="4i">4</a></td> +<td class="tdc_top">\(K_2\)</td> +<td class="tdc_top">\(Ti_2\); \(Ca_3\); Ti, \(Fe_4\)</td> +<td class="tdl"></td> +</tr><tr> +<td class="tdl_top"></td> +<td class="tdc_top"><a id="5i">5</a></td> +<td class="tdc_top">(\(M_a\))</td> +<td class="tdc_top">\(Ti_2\); \(Ca_4\); Cr 5; +\(Ti_1\); \(Ti_2\); \(Fe_1\)</td> +<td class="tdl_top">Ca and Cr cause rise at \(M_a\). Ti obliterated</td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"><a id="6i">6</a></td> +<td class="tdc">(none)</td> +<td class="tdc">\(Ti_2\); \(Cr_7\)</td> +<td class="tdl">Cr (ultimate) line predominates</td> +</tr><tr> +<td class="tdl_top"></td> +<td class="tdc_top"><a id="7i">7</a></td> +<td class="tdc_top">none</td> +<td class="tdc_top">\(Fe_4\); \(Co_4\); \(Fe_4\); \(Ti_4\)</td> +<td class="tdl">Possibly an enhanced line accounts +for maximum near \(F_5\)?</td> +</tr><tr> +<td class="tdl_top"></td> +<td class="tdc_top"><a id="8i">8</a></td> +<td class="tdc_top">\(G_0\)(\(F_5\)?)</td> +<td class="tdc_top">\(Mg_5\); \(Ti_6\)</td> +<td class="tdl_top">Mg accounts for maximum at \(M_a\)</td> +</tr><tr> +<td class="tdl_top"></td> +<td class="tdc_top"><a id="9i">9</a></td> +<td class="tdc_top">\(G_0\)(\(F_5\)?)</td> +<td class="tdc_top">\(Ti_4\)</td> +<td class="tdl_top">Unblended</td> +</tr><tr> +<td class="tdl_top"></td> +<td class="tdc_top"><a id="10i">10</a></td> +<td class="tdc_top">\(G_0\)(\(F_5\)?)</td> +<td class="tdc_top">Ti, -5</td> +<td class="tdl_top">Probably unblended</td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"><a id="11i">11</a></td> +<td class="tdc">\(F_5\)</td> +<td class="tdc">\(Fe_3\); \(Ti_5\)</td> +<td class="tdl">Maximum at \(K_2\) due to Fe</td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"><a id="12i">12</a></td> +<td class="tdc">\(F_5\)?</td> +<td class="tdc">\(Ti_3\); V, \(Zr_2\)</td> +<td class="tdl">Blended with Ti. See Note 1</td> +</tr><tr> +<td class="tdl_top"></td> +<td class="tdc_top"><a id="13i">13</a></td> +<td class="tdc_top">?</td> +<td class="tdc_top">\(Fe_5\); \(Cr_3\); \(Ti_4\)</td> +<td class="tdl_top">Fe predominates. Maximum uncertain</td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"><a id="14i">14</a></td> +<td class="tdc">\(F_5\)</td> +<td class="tdc">\(Ti_3\); \(Fe_4\)</td> +<td class="tdl">Rise at \(M_a\) due to Fe. In \(G\) band</td> +</tr><tr> +<td class="tdl_top"></td> +<td class="tdc_top"><a id="15i">15</a></td> +<td class="tdc_top">\(G_0\)</td> +<td class="tdc_top">\(Ca_3\); \(Fe_6\)</td> +<td class="tdl">Rowland gives no Ti. Other lines account +for later maximum. In \(G\) band</td> +</tr><tr> +<td class="tdl_top"></td> +<td class="tdc_top"><a id="16i">16</a></td> +<td class="tdc_top">?</td> +<td class="tdc_top">\(Ti_2\); \(Fe_2\); \(Ca_2\)</td> +<td class="tdl_top">Maximum undetermined. In \(G\) band</td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"><a id="17i">17</a></td> +<td class="tdc">\(F_5\)</td> +<td class="tdc">\(Ti_3\)</td> +<td class="tdl">Unblended</td> +</tr><tr> +<td class="tdl_top"></td> +<td class="tdc_top"><a id="18i">18</a></td> +<td class="tdc_top">\(G_0\)(\(F_5\)?)</td> +<td class="tdc_top">\(Cr_5\); \(Ti_1\); \(Ti_2\)</td> +<td class="tdl_top">Cr accounts for strength in \(M_a\)</td> +</tr><tr> +<td class="tdl">V</td> +<td class="tdc"><a id="1j">1</a></td> +<td class="tdc">\(K_5\)</td> +<td class="tdc">\(Ti_3\); V, \(Zr_2\)</td> +<td class="tdl">Ti and Ti+ lines blended. V probably obliterated</td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"><a id="2j">2</a></td> +<td class="tdc">none</td> +<td class="tdc">\(V_4\)</td> +<td class="tdl">Unblended</td> +</tr><tr> +<td class="tdl_top"></td> +<td class="tdc_top"><a id="3j">3</a></td> +<td class="tdc_top">none</td> +<td class="tdc_top">Ti, \(Ni_2\); \(V_0\)</td> +<td class="tdl">V probably effective at low temperatures, as these +are the ultimate lines</td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"><a id="4j">4</a></td> +<td class="tdc">none</td> +<td class="tdc">\(La_1\) N; \(V_0\)</td> +<td class="tdl"></td> +</tr><tr> +<td class="tdl">Cr</td> +<td class="tdc"><a id="1k">1</a></td> +<td class="tdc">\(K_5\)</td> +<td class="tdc">\(Cr_3\)</td> +<td class="tdl">Unblended</td> +</tr><tr> +<td class="tdl_top"></td> +<td class="tdc_top"><a id="2k">2</a></td> +<td class="tdc_top">none</td> +<td class="tdc_top">\(Mg_5\) Nd? \(Cr_5\); \(Fe_4\)</td> +<td class="tdl_top">Unblended</td> +</tr><tr> +<td class="tdl_top"></td> +<td class="tdc_top"><a id="3k">3</a></td> +<td class="tdc_top">none</td> +<td class="tdc_top">\(Ca_4\); \(Cr_5\); \(Ti_1\); \(Ti_3\)</td> +<td class="tdl_top">Cr probably predominates</td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"><a id="4k">4</a></td> +<td class="tdc">none</td> +<td class="tdc">\(Ti_2\); Cr \(_7d\)?</td> +<td class="tdl">Cr predominates</td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"><a id="5k">5</a></td> +<td class="tdc">none</td> +<td class="tdc">\(Cr_8\)</td> +<td class="tdl">Unblended</td> +</tr><tr> +<td class="tdl">Mn</td> +<td class="tdc"><a id="1l">1</a></td> +<td class="tdc">none</td> +<td class="tdc">\(Mn_3\)</td> +<td class="tdl">Unblended</td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"><a id="2l">2</a></td> +<td class="tdc">none</td> +<td class="tdc">\(Mn_2\); \(Fe_8\)</td> +<td class="tdl">Fe predominates?</td> +</tr><tr> +<td class="tdl_top"></td> +<td class="tdc_top"><a id="3l">3</a></td> +<td class="tdc_top">none</td> +<td class="tdc_top">\(Fe_3\); \(Mn_5\); Zr, -1</td> +<td class="tdl_top"></td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"><a id="4l">4</a></td> +<td class="tdc">none</td> +<td class="tdc">\(Co_2\); Mn \(_4d\)?</td> +<td class="tdl">Mn predominates</td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"><a id="5l">5</a></td> +<td class="tdc">none</td> +<td class="tdc">Mn-Fe \(_6d\)?</td> +<td class="tdl"></td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"><a id="6l">6</a></td> +<td class="tdc">none</td> +<td class="tdc">Fe-Mn \(_6d\)?</td> +<td class="tdl"><span class="pagenum" id="Page_129">[Pg 129]</span></td> +</tr><tr> +<td class="tdl_top"></td> +<td class="tdc_top"><a id="7l">7</a></td> +<td class="tdc_top">\(M_a\)</td> +<td class="tdc_top">Fe, \(Ti_5\); \(Mn_4\); \(Mn_5\)</td> +<td class="tdl_top">Mn predominates?</td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"><a id="8l">8</a></td> +<td class="tdc">\(K_5\)</td> +<td class="tdc">Fe-Mn 6</td> +<td class="tdl"></td> +</tr><tr> +<td class="tdl_top"></td> +<td class="tdc_top"><a id="9l">9</a></td> +<td class="tdc_top">\(M_a\)</td> +<td class="tdc_top">\(Fe_2\); Co, \(Mn_3\); \(Fe_1\); +V, Ca \(_3d\)?</td> +<td class="tdl"></td> +</tr><tr> +<td class="tdl">Fe</td> +<td class="tdc"><a id="1m">1</a></td> +<td class="tdc">\(K_2\)</td> +<td class="tdc">Mn-Fe</td> +<td class="tdl">Effectively unblended</td> +</tr><tr> +<td class="tdl_top"></td> +<td class="tdc_top"><a id="2m">2</a></td> +<td class="tdc_top">(\(K_2\))</td> +<td class="tdc_top">\(Fe_3\), \(Fe_5\)</td> +<td class="tdl">No. 2 the weaker line, Mn+ affects +the line at and before \(A_5\), producing maximum at \(A_3\). +See No. 27</td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"><a id="3m">3</a></td> +<td class="tdc">none</td> +<td class="tdc">Fe-Mn, 3 \(N_d\)?</td> +<td class="tdl">Effectively unblended</td> +</tr><tr> +<td class="tdl_top"></td> +<td class="tdc_top"><a id="4m">4</a></td> +<td class="tdc_top">none</td> +<td class="tdc_top">Sc, Fe? 3; \(Zr_0\); V, +\(Mn_2\)</td> +<td class="tdl_top">Y+ accounts for maximum at \(G_0\)</td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"><a id="5m">5</a></td> +<td class="tdc">-</td> +<td class="tdc">Sr+</td> +<td class="tdl">Due entirely to Sr+</td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"><a id="6m">6</a></td> +<td class="tdc">\(K_2\)?</td> +<td class="tdc">\(Mn_2\); \(Fe_8\); -3</td> +<td class="tdl">Maximum at \(F_5\) due to Fe+</td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"><a id="7m">7</a></td> +<td class="tdc">\(K_2\)</td> +<td class="tdc">\(Fe_{10}\)</td> +<td class="tdl">Unblended</td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"><a id="8m">8</a></td> +<td class="tdc">\(K_2\)</td> +<td class="tdc">\(Fe_{15}\)</td> +<td class="tdl">Unblended</td> +</tr><tr> +<td class="tdl_top"></td> +<td class="tdc_top"><a id="9m">9</a></td> +<td class="tdc_top">(\(M_a\))</td> +<td class="tdc_top">\(Fe_5\); \(Cr_3\); \(Ti_4\)</td> +<td class="tdl_top">Ti+ (\(^2D-^2P\)) causes maximum at +\(F_5\); possibly Cr (\(^6D-^6F\)) causes +rise at \(M_a\)</td> +</tr><tr> +<td class="tdl_top"></td> +<td class="tdc_top"><a id="10m">10</a></td> +<td class="tdc_top">(\(M_a\))</td> +<td class="tdc_top">\(Ti_3\); \(Ti_2\); \(Fe_2\)</td> +<td class="tdl_top">Ti predominates?</td> +</tr><tr> +<td class="tdl_top"></td> +<td class="tdc_top"><a id="11m">11</a></td> +<td class="tdc_top">\(K_2\)</td> +<td class="tdc_top">\(Fe_8\); \(Sc_4\); Ti, \(Zr_1\)</td> +<td class="tdl_top">Fe probably predominates</td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"><a id="12m">12</a></td> +<td class="tdc">none</td> +<td class="tdc">\(Ca_3\); \(Fe_6\)</td> +<td class="tdl">Ca produces rise in late classes?</td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"><a id="13m">13</a></td> +<td class="tdc">\(K_2\)</td> +<td class="tdc">\(Fe_{15}\)</td> +<td class="tdl">Unblended. Rise at \(M_a\) unexplained</td> +</tr><tr> +<td class="tdl_top"></td> +<td class="tdc_top"><a id="14m">14</a></td> +<td class="tdc_top">\(K_2\)</td> +<td class="tdc_top">Fe \(_3d\)? \(Fe_{10}\)</td> +<td class="tdl_top">Unblended. Rise at \(M_a\) unexplained, unless due +to second Fe line</td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"><a id="15m">15</a></td> +<td class="tdc">\(K_2\)</td> +<td class="tdc">\(Fe_8\); \(Fe_8\)</td> +<td class="tdl">Rise at \(M_a\) unexplained. See No. 25</td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"><a id="16m">16</a></td> +<td class="tdc">\(K_0\)</td> +<td class="tdc">\(Fe_{15}\); \(Fe_4\)</td> +<td class="tdl"></td> +</tr><tr> +<td class="tdl_top"></td> +<td class="tdc_top"><a id="17m">17</a></td> +<td class="tdc_top">\(K_5\)</td> +<td class="tdc_top">\(Fe_{10}\); -3</td> +<td class="tdl_top">Maximum at \(K_5\) due to unknown +line?</td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"><a id="18m">18</a></td> +<td class="tdc">\(K_0\)</td> +<td class="tdc">\(Fe_1\); \(Fe_{15}\)</td> +<td class="tdl"></td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"><a id="19m">19</a></td> +<td class="tdc">\(K_2\)</td> +<td class="tdc">\(Fe_4\); \(Fe_{20}\)</td> +<td class="tdl"></td> +</tr><tr> +<td class="tdl_top"></td> +<td class="tdc_top"><a id="20m">20</a></td> +<td class="tdc_top">\(K_2\)</td> +<td class="tdc_top">\(Mn_{2,1}\); \(Co_5\); \(Fe_{30}\)</td> +<td class="tdl_top">Fe predominates</td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"><a id="21m">21</a></td> +<td class="tdc">\(K_2\)</td> +<td class="tdc">\(Fe_7\); ? 3; \(Fe_1\); -1, +1, 1</td> +<td class="tdl"></td> +</tr><tr> +<td class="tdl_top"></td> +<td class="tdc_top"><a id="22m">22</a></td> +<td class="tdc_top">\(K_2\)</td> +<td class="tdc_top">\(Ca_3\); Ti, \(Fe_4\); \(Ti_2\)</td> +<td class="tdl_top">Rise at \(M_a\) due to Ca?</td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"><a id="23m">23</a></td> +<td class="tdc">\(K_2\)</td> +<td class="tdc">\(Fe_6\); \(Fe_{15}\)</td> +<td class="tdl">No. 23 the weaker line</td> +</tr><tr> +<td class="tdl_top"></td> +<td class="tdc_top"><a id="24m">24</a></td> +<td class="tdc_top">\(K_2\)</td> +<td class="tdc_top">\(Fe_2\); \(Fe_3\); \(Fe_{10}\)</td> +<td class="tdl_top">No. 24 the strongest line</td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"><a id="25m">25</a></td> +<td class="tdc">\(K_2\)</td> +<td class="tdc">\(Fe_8\)</td> +<td class="tdl">See No. 15. Rise at \(M_a\) unexplained</td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"><a id="26m">26</a></td> +<td class="tdc">?</td> +<td class="tdc">\(Fe_2\); \(Fe_5\)</td> +<td class="tdl"></td> +</tr><tr> +<td class="tdl_top"></td> +<td class="tdc_top"><a id="27m">27</a></td> +<td class="tdc_top">\(K_2\)</td> +<td class="tdc_top">\(Fe_3\); \(Fe_5\)</td> +<td class="tdl_top">The stronger line. Responsible also +for the maximum of line 2</td> +</tr><tr> +<td class="tdl_top"></td> +<td class="tdc_top"><a id="28m">28</a></td> +<td class="tdc_top">\(K_2\)</td> +<td class="tdc_top">\(V_2\); \(Fe_4\); \(V_2\); \(Fe_3\); +\(V_2\)</td> +<td class="tdl_top">Rise at \(M_a\) due to V</td> +</tr><tr> +<td class="tdl_top"></td> +<td class="tdc_top"><a id="29m">29</a></td> +<td class="tdc_top">none</td> +<td class="tdc_top">\(Cr_5\); \(Mn_5\); \(Fe_4\)</td> +<td class="tdl_top">Cr and Mn predominate. Cr (ultimate) +line responsible for rise at \(M_a\) +<span class="pagenum" id="Page_130">[Pg 130]</span></td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"><a id="30m">30</a></td> +<td class="tdc">\(F_5\)</td> +<td class="tdc">\(Ti_3\); \(Fe_4\)</td> +<td class="tdl">Maximum at \(F_5\) due to Fe+</td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"><a id="31m">31</a></td> +<td class="tdc">\(M_a\)</td> +<td class="tdc">\(Fe_5\); \(Ca_4\)</td> +<td class="tdl">Ca produces rise at \(M_a\)</td> +</tr><tr> +<td class="tdl_top"></td> +<td class="tdc_top"><a id="32m">32</a></td> +<td class="tdc_top">\(M_a\)</td> +<td class="tdc_top">\(Fe_2\); \(Fe_2\); \(Fe_2\)</td> +<td class="tdl_top">Rise at \(M_a\) unexplained</td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"><a id="33m">33</a></td> +<td class="tdc">\(K_2\)</td> +<td class="tdc">Sr+</td> +<td class="tdl">Due entirely to Sr+</td> +</tr><tr> +<td class="tdl_top"></td> +<td class="tdc_top"><a id="34m">34</a></td> +<td class="tdc_top">\(K_2\)-\(K_5\)</td> +<td class="tdc_top">\(Fe_3\); Fe? 3; V-Fe?\(_3\); +\(Fe_5\)</td> +<td class="tdl"></td> +</tr><tr> +<td class="tdc"></td> +<td class="tdc_top"><a id="35m">35</a></td> +<td class="tdc_top">?</td> +<td class="tdc_top">\(Fe_4\); Fe, -3; \(Mn_3\); +\(Co_3\); -, 1; Fe-Cr 3</td> +<td class="tdl_top">Too heavily blended</td> +</tr><tr> +<td class="tdl_top"></td> +<td class="tdc_top"><a id="36m">36</a></td> +<td class="tdc_top">\(G_0\)</td> +<td class="tdc_top">Co \(_4d\)?; \(Fe_4\); \(Ti_4\)</td> +<td class="tdl_top">Maximum at \(G_0\) unexplained. Rise +at \(M_a\) due to Ti (ultimate line)</td> +</tr><tr> +<td class="tdl_top"></td> +<td class="tdc_top"><a id="37m">37</a></td> +<td class="tdc_top">\(K_2\)</td> +<td class="tdc_top">Cr, La, Mn, Ni, \(Fe_2\); +Ti, Fe2; Al?; Fe2</td> +<td class="tdl_top">See Rowland, p. 37. An Fe+ line +responsible</td> +</tr><tr> +<td class="tdl_top"></td> +<td class="tdc_top"><a id="38m">1</a><a id="38a">1</a></td> +<td class="tdc_top">\(K_5\)</td> +<td class="tdc_top">\(Fe_2\); \(Fe_1\); \(Ni_2\)</td> +<td class="tdl_top"></td> +</tr><tr> +<td class="tdl_top"></td> +<td class="tdc_top"><a id="39m">39</a></td> +<td class="tdc_top">none</td> +<td class="tdc_top">\(Fe_4\); Fe, \(Mn_3\); Nd?</td> +<td class="tdl_top">Rise at \(M_a\) unexplained</td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"><a id="40m">40</a></td> +<td class="tdc">(\(M_a\))</td> +<td class="tdc">\(Fe_4\); \(Ag_3\)</td> +<td class="tdl">Rise at \(M_a\) probably due to Ag</td> +</tr><tr> +<td class="tdl_top"></td> +<td class="tdc_top"><a id="41m">41</a></td> +<td class="tdc_top">\(F_5\)</td> +<td class="tdl_top">\(Fe_4\); \(Fe_3\); -3; -3</td> +<td class="tdl_top">Maximum certainly due to Fe+. +Neutral Fe causes rise in cool classes</td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"><a id="42m">42</a></td> +<td class="tdc">\(F_5\)</td> +<td class="tdl">\(Fe_3\); -3; -1; -1N</td> +<td class="tdl">Maximum due to ionized iron</td> +</tr><tr> +<td class="tdl_top"></td> +<td class="tdc_top"><a id="43m">43</a></td> +<td class="tdc_top">\(F_5\)</td> +<td class="tdl_top">\(Mn_2\); \(Fe_8\)</td> +<td class="tdl_top">Maximum due to Fe+; later rise +perhaps due to Mn</td> +</tr><tr> +<td class="tdl">Zn</td> +<td class="tdc"><a id="1n">1</a></td> +<td class="tdc">\(G_0\)</td> +<td class="tdl">\(Zn_3\)</td> +<td class="tdl">Unblended</td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"><a id="2n">2</a></td> +<td class="tdc">\(G_0\)</td> +<td class="tdl">\(Zn_3\)</td> +<td class="tdl">Unblended</td> +</tr><tr> +<td class="tdl_top">Sr</td> +<td class="tdc_top"><a id="1o">1</a></td> +<td class="tdc_top">none</td> +<td class="tdl_top">\(Sr_1\); \(Fe_4\)</td> +<td class="tdl_top">Fe probably predominates, except +perhaps at the lowest temperatures</td> +</tr><tr> +<td class="tdl_top"></td> +<td class="tdc_top"><a id="2o">2</a></td> +<td class="tdc_top">\(K_2\)</td> +<td class="tdl_top">\(Fe_2\); Sr \(_5d\)?; Fe \(_3d\)?</td> +<td class="tdl_top">Fe probably strong, but Sr responsible +for part of maximum at \(K_2\)</td> +</tr><tr> +<td class="tdl_top"></td> +<td class="tdc_top"><a id="3o">3</a></td> +<td class="tdc_top">\(M_a\)</td> +<td class="tdl_top">Fe, \(Zr_2\); \(Fe_4\); \(Fe_2\); +La, \(Y_1\) Nd? \(Sr_8\); +\(Fe_4\); \(Ti_3\)</td> +<td class="tdl_top">Maximum uncertain owing to heavy +blending</td> +</tr><tr> +<td class="tdl">Y</td> +<td class="tdc"><a id="1p">1</a></td> +<td class="tdc">\(G_0\)</td> +<td class="tdl">\(Cr_1\); -1; Sc, \(Fe_3\)</td> +<td class="tdl">Y+ gives the maximum</td> +</tr><tr> +<td class="tdl_top"></td> +<td class="tdc_top"><a id="2p">2</a></td> +<td class="tdc_top">\(F_5\)?</td> +<td class="tdl_top">\(Fe_3\); -3</td> +<td class="tdl_top">Maximum ill determined, but probably +due to Y+</td> +</tr><tr> +<td class="tdl_top"></td> +<td class="tdc_top"><a id="3p">3</a></td> +<td class="tdc_top">\(G_0\)?</td> +<td class="tdl_top">-1</td> +<td class="tdl_top">Remark in Rowland:--in zircon but +not in Zr</td> +</tr><tr> +<td class="tdl">Ba</td> +<td class="tdc"><a id="1q">1</a></td> +<td class="tdc">none</td> +<td class="tdl">\(Ba_8\)</td> +<td class="tdl">Unblended</td> +</tr> + </tbody> +</table> + + +<p class="nindc space-above2"> +CONSISTENCY OF RESULTS</p> + + +<p>The preceding tabulation summarizes the present state of the +observational material bearing on the positions of the maxima of +absorption lines. The comparison with theory is an important and +difficult problem. The theoretical formulae contain as variables the +temperature and the pressure; and the +<span class="pagenum" id="Page_131">[Pg 131]</span> fractional concentration, +\(n_r\), is very sensitive to changes in both these variables. It would +therefore be possible to satisfy almost any observations by varying +the two quantities jointly; but this procedure would furnish no useful +test of the theory. The test made in the present chapter will involve +the calculation of the temperature scale, with the partial electron +pressure, \(P_e\), assumed constant.</p> + +<figure class="figcenter" id="i008"> +<img src="images/i008.jpg" width="1500" height="1029" alt="i008"> +<figcaption class="caption"> + +<p>Figure 8</p> + +<p>Reproduced from H.C. 256, 1924. Comparison between observation +and ionization theory for the hotter stars. The observations are +contained in the upper part of the diagram, and the theoretical curves +(based on a partial electron pressure +\(\displaystyle{1.3~ \times 10^{-4}~\text{atmospheres}}\) are +given in the lower part of the figure. For the upper half, ordinates +are the observed intensities contained in <a href="#TABLE_XIX">Table XIX</a>; abscissae are +spectral classes from the Draper Catalogue. In the lower part of the +figure, ordinates are logarithms of computed fractional concentrations; +abscissae are temperatures in thousands of degrees. The abscissae of +the upper and lower diagrams have been adjusted so that the observed +and computed maxima coincide, thus forming a preliminary temperature +scale.</p></figcaption> +</figure> + +<p>It is certain that this condition is not satisfied in practice, +and a more rigorous treatment, which allows for the differences in +partial electron pressure, is contained in the chapter that follows. +But with the object of examining the consistency of the derived +temperature scale, the present test is made under the assumption that +the partial electron pressure is constant and equal to about +<span class="pagenum" id="Page_132">[Pg 132]</span> +\(\displaystyle{1.3~\times 10^{-4}~ \text{atmospheres}}\).</p> + +<p>The resulting scale of temperatures for the reversing layers of +the corresponding classes is contained in the table that follows. +Successive columns contain the element that is utilized, the spectral +class at which its lines attain maximum, and the corresponding +temperature derived from the equations of <a href="#CHAPTER_VII">Chapter VII</a>.</p> + +<table class="autotable"> +<thead><tr> +<th class="tdc">Element</th> +<th class="tdc">Maximum</th> +<th class="tdc">Temperature</th> +<th class="tdc">Element</th> +<th class="tdc">Maximum</th> +<th class="tdc">Temperature</th> +</tr> +</thead> +<tbody><tr> +<td class="tdl">He+</td> +<td class="tdc">\(O\)</td> +<td class="tdc">35000°</td> +<td class="tdl">Ti</td> +<td class="tdc">\(K_2-K_5\)</td> +<td class="tdc">3500°</td> +</tr><tr> +<td class="tdl">Si+++</td> +<td class="tdc">\(O\)</td> +<td class="tdc">25000</td> +<td class="tdl">Mn</td> +<td class="tdc">\(K_2\)</td> +<td class="tdc">5000</td> +</tr><tr> +<td class="tdl">Si++</td> +<td class="tdc">\(B_2-B_1\)</td> +<td class="tdc">18000</td> +<td class="tdl">Fe</td> +<td class="tdc">\(K_2\)</td> +<td class="tdc">5000</td> +</tr><tr> +<td class="tdl">He</td> +<td class="tdc">\(B_3\)</td> +<td class="tdc">10000</td> +<td class="tdl">V</td> +<td class="tdc">\(K_5\)</td> +<td class="tdc">3500</td> +</tr><tr> +<td class="tdl">C+</td> +<td class="tdc">\(B_3\)</td> +<td class="tdc">16000</td> +<td class="tdl">Cr</td> +<td class="tdc">\(K_5\)</td> +<td class="tdc">3500</td> +</tr><tr> +<td class="tdl">Si+</td> +<td class="tdc">\(A_0\)</td> +<td class="tdc">11000</td> +<td class="tdl">Sr+</td> +<td class="tdc">\(M_a\)</td> +<td class="tdc">6000</td> +</tr><tr> +<td class="tdl">H</td> +<td class="tdc">\(A_0\)</td> +<td class="tdc">10000</td> +<td class="tdl">Ba+</td> +<td class="tdc">None</td> +<td class="tdc">5500</td> +</tr><tr> +<td class="tdl"><a href="#iii">*</a>Zn</td> +<td class="tdc">\(G_0\)</td> +<td class="tdc">8000</td> +<td class="tdl">Ca</td> +<td class="tdc">\(M_a\)</td> +<td class="tdc">4500</td> +</tr><tr> +<td class="tdl"><a href="#iii">*</a>Ca+</td> +<td class="tdc">\(K_0\)</td> +<td class="tdc">6000</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +</tr> + </tbody> +</table> + +<p class="nindc"> +<a id="iii">*</a> Estimates by Menzel, H. C. 258, 1924.</p> + + +<div class="footnotes"><h3>FOOTNOTES:</h3> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_403" href="#FNanchor_403" class="label">[403]</a> +Payne, H. C. 256, 263, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_404" href="#FNanchor_404" class="label">[404]</a> +Menzel, H. C. 258, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_405" href="#FNanchor_405" class="label">[405]</a> +Harper and Young, Pub. Dom. Ap. Obs., 3, 3, 1925.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_406" href="#FNanchor_406" class="label">[406]</a> +Chapter X, <a href="#Page_142">p. 142</a>.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_407" href="#FNanchor_407" class="label">[407]</a> +Menzel, H. C. 258, 1924.</p> + +</div> +</div> + + +<hr class="chap x-ebookmaker-drop"> + +<div class="chapter"> +<p><span class="pagenum" id="Page_133">[Pg 133]</span></p> +<h2 class="nobreak" id="CHAPTER_IX">CHAPTER IX<br> +THE IONIZATION TEMPERATURE SCALE</h2> +</div> + +<p class="nind"> +A preliminary application of the observed maxima of absorption lines, +in the formation of a stellar temperature scale, was given at the +end of the preceding chapter. The temperatures were obtained on the +assumption that \(P_e\), the partial electron pressure in the reversing +layer, was constant for all lines and equal to +\(\displaystyle{1.3~\times 10^{-4}~ \text{atmospheres}}\). +Striking inconsistencies appear in this preliminary table of +temperatures. As Menzel<a id="FNanchor_408" href="#Footnote_408" class="fnanchor">[408]</a> has remarked, the maxima of most of the +metallic arc lines occur in stars cooler than the ionization theory, +on the stated assumptions, would predict. The ultimate lines of the +ionized atoms of calcium, strontium, and barium show especially +large inconsistencies. The temperatures of the maxima for these +atoms, deduced from the ionization formula on the assumption that +\(\displaystyle{P_e = 1.3~ \times 10^{-4}~ \text{atmospheres}}\), are +about 3000° higher than the measured temperatures of the classes at +which the maxima occur, as deduced from the color indices.</p> + +<p>The following suggestion has been advanced by Fowler and Milne<a id="FNanchor_409" href="#Footnote_409" class="fnanchor">[409]</a> +to account for the observed deviations of Ca+, Sr+, and Ba+. “For the +maximum of the principal line of an ionized atom, the fraction of atoms +in the required state is almost unity.... On the other hand ... at the +maxima of subordinate lines the fraction of atoms in the required state +is from \(10^{-3}\) to \(10^{-5}\).... Thus atoms in the required +state are \(10^{3}\) to \(10^{6}\) times as abundant for intense +principal lines as for intense subordinate lines. It follows that +principal lines must originate at much higher levels in the stellar +atmosphere than subordinate lines, and consequently at much smaller +pressures.”</p> + +<p><span class="pagenum" id="Page_134">[Pg 134]</span></p> + +<p>It appears that the behavior of the ionized atoms of the alkaline +earths can be satisfactorily explained in this way. The further +suggestion was made that a similar effect might be expected for atoms +of low excitation potential, such as manganese and magnesium.</p> + +<p>The possibility of varying \(P_e\) as well as \(T\) in the formula +for the theoretical maximum places the investigation on a rather +different footing. Any temperature (within wide limits) may now be +obtained for the theoretical maximum of a line by appropriately varying +the partial pressure. The stellar temperature scale cannot, in such +a case, be fixed merely from a knowledge of the critical potentials +and the observed maxima, without introducing other considerations. +It is necessary to find a way of determining the appropriate partial +pressures.</p> + +<p>The procedure that will here be followed consists essentially in a +calibration and an extrapolation. The temperature scale from \(M_a\) +to \(F_0\) is regarded as known from spectrophotometric data. Within +this range, the theoretical and observed maxima are compared. The +possibility of finding a value of \(P_e\) appropriate to a given +atomic state is next examined. Finally, a method of estimating \(P_e\) +will be justified for the cooler stars, within the limits of accuracy +permitted by the data, and will be extended by simple extrapolation to +the formation of a temperature scale for the hotter stars, where the +temperatures cannot be safely estimated from the color indices.</p> + +<p>The salient point is that complete absorption will occur for any line +at a depth that is inversely proportional to the abundance of the +corresponding state of the atom. No light in this wave-length reaches +the exterior from any lower level, and the deepest level from which +the line originates therefore forms a lower boundary to the effective +portion of the atom in question. The “effective level” from which +a line comes is probably best regarded as the level at which the +effective atoms above the “lower boundary” have their median frequency. +Clearly the partial pressure will differ at different effective levels, +and thus abundance has a direct influence on the appropriate value of +<span class="pagenum" id="Page_135">[Pg 135]</span> +the partial pressure.</p> + +<p>The theory with which we have so far been concerned deals with the +<i>excited fraction</i> of the total amount of the element which is +present. A knowledge of this quantity suffices for specifying the +variation of intensity for the lines of any one element. But the +absolute abundance of a given atomic state varies jointly with the +fractional concentration of the appropriate state and the total amount +of the element present. Now, for the first time, the absolute abundance +of different atomic species becomes of possible importance, as a +factor affecting the depth from which radiation corresponding to the +given atom will penetrate. Fowler and Milne<a id="FNanchor_410" href="#Footnote_410" class="fnanchor">[410]</a> rightly claimed that +their method of maxima eliminated questions of relative abundance, “if +\(P_e\) can be regarded as known ... [and constant]. The proper value +of \(P_e\) must be a function of the abundance of the atom in question +relative to free electrons.”</p> + +<p>The question of relative abundances of elements in the reversing +layer is discussed<a id="FNanchor_411" href="#Footnote_411" class="fnanchor">[411]</a> in <a href="#CHAPTER_XIII">Chapter XIII</a>. It may be mentioned that the +abundances there deduced depend upon estimates of marginal appearance. +Probably all lines are unsaturated at <i>marginal appearance</i>, that +is, there are not enough suitable atoms present completely to absorb +<i>all</i> the incident light of the appropriate wave-length. Hence all +suitable atoms present, as far down as the photosphere, where general +opacity begins to render the gas hazy, are actually contributing to +the line. At marginal appearance, then, all the intensity phenomena +are probably due to pure abundance, and considerations of level are +eliminated. The deduced abundances are therefore independent of +effects such as are discussed in the present chapter, and the results +of <a href="#CHAPTER_XIII">Chapter XIII</a> may be cited as giving evidence that the stellar +abundances, for all the atoms here to be considered except barium, have +a range with only a factor of ten, which is negligible in comparison +with the quantities to be discussed. The relative abundance of +<span class="pagenum" id="Page_136">[Pg 136]</span> +different atomic species will therefore be neglected in what follows, +although, with more accurate data than are now available, it should +become a factor of importance.</p> + +<p>Fractional concentrations, as derived from the ionization formula, +govern the effective level at which absorption takes place. Fowler +and Milne, as was pointed out earlier, suggested that the higher the +fractional concentration at maximum, the higher the level and the lower +the partial pressure from which the line originates. They suggested +that the pressure for a principal line at maximum is from \(10^{-3}\) +to \(10^{-53}\) of the corresponding value for a subordinate line.</p> + +<p>The assumption now introduced is, in effect, that the absorbing +efficiency of individual atoms is the same. The partial pressure at the +level from which a line originates should then vary inversely as the +fractional concentration at maximum. In other words, the product +\[ +P_e~\times~ n_{r(max)} +\] +should be constant, when \(P_e\) is deduced from the class at which the +<i>observed maximum</i> occurs.</p> + +<p>The quantity \(n_{r(max)}\) depends primarily on the excitation +potential, and varies but slowly with \(T_{max}\). It is given by the +expression[iii] +\[ +n_{r(\max )}=\frac{\chi_{1}^{(r)}+\frac{5}{2} k T_{\max }}{\chi_{1}+\frac{5}{2} k T_{\max }} \cdot \frac{q_{1}^{(r)} +e^{\left(x_{1}-\chi_{1}^{{}(r)}\right) / k T_{\max }}}{b_{1}\left(T_{\max }\right)} +\]</p> + +<p>[iii] For notation, see Chapter VII, <a href="#Page_106">p. 106</a>.</p> + +<p>For subordinate lines, \(P_e\) is given by the expression +\[ +\frac{\chi_{1}^{(r)}+\frac{5}{2} k T}{\chi_{1}-\chi_{1}^{(r)}} \cdot \frac{(2 \pi m)^{\frac{3}{2}}(k T)^{\frac{5}{2}} +\sigma_{1}}{h^{3} b_{1}(T)} e^{-x_{1} / k T} +\] +and this quantity is extremely sensitive to change in \(T_{max}\).</p> + +<p>For ultimate lines, where the excitation potential is equal to zero, +and \(n_{r(max)}\) accordingly reduces to unity, the value of \(P_e\) +should be <i>equal</i> to the constant product predicted in a previous +<span class="pagenum" id="Page_137">[Pg 137]</span> +paragraph. Fowler and Milne suggested a partial electron pressure +of \(10^{-7}\) to \(10^{-8}\) for Ca+ on the basis of a maximum at +\(K_0\), assumed temperature 4500°. This is the effective temperature +of the class, deduced spectrophotometrically, and “the reversing layer +should be at a lower temperature—its average temperature should be in +the neighborhood of, or somewhat lower than, the Schwarzschild boundary +temperature,[<a href="#iv">iv</a>] which is some 15-20 per cent lower than the effective +temperature.” The value 4000° is therefore adopted here for \(K_{0}\). +For this value \(P_e\) becomes \(3.24~ \times~ 10^{-9}\) for Ca+; for +Sr+ (\(K_2\), 35000°), \(P_e = 4.6~ \times~ 10^{-10}\), and for Ba+ +(Ma? 3000°), \(P_e = 6~ \times~ 10^{-11}\). The maximum for Sr+ is the +best determined of the three, as the Ca+ lines are too strong and too +far into the violet for an accurate estimate among the cooler stars, +and the Ba+ line is rather faint, and is heavily blended. The constant +product may then be expected to be of the order of \(10^{-10}\).</p> + +<p>The prediction is examined in the table that follows. The temperature +of the class at which the lines attain maximum is assumed from +spectrophotometric data, and is expressed to the nearest five hundred +degrees.</p> + +<h2><a id="TABLE_XX">TABLE XX</a></h2> + +<table class="autotable"> +<thead><tr> +<th class="tdc bb bt2 br">Atom </th> +<th class="tdc_ws1 bb bt2 br"> Ionization<br> +Potential </th> +<th class="tdc_ws1 bb bt2 br"> Excitation<br> +Potential </th> +<th class="tdc bb bt2 br"> Max. </th> +<th class="tdc bb bt2 br"> \(T_{max}\) </th> +<th class="tdc bb bt2 br">\(log~ P_e\)</th> +<th class="tdc bb bt2 br"> \(log~ n_r\) </th> +<th class="tdc bb bt2"> Sum </th> +</tr> +</thead> +<tbody><tr> +<td class="tdl br">Mg+</td> +<td class="tdc br">14.97</td> +<td class="tdc br">8.83</td> +<td class="tdl br">\(A_3\)</td> +<td class="tdc br">9000°</td> +<td class="tdc br">\(\overline{6}.99\)</td> +<td class="tdc br">5.32</td> +<td class="tdc">\(\overline{10}.3\)</td> +</tr><tr> +<td class="tdl br">Ca</td> +<td class="tdc br">6.09</td> +<td class="tdc br">1.88</td> +<td class="tdl br">\(M_a\)</td> +<td class="tdc br">3000</td> +<td class="tdc br">\(\overline{8}.63\)</td> +<td class="tdc br">3.64</td> +<td class="tdc">\(\overline{10}.3\)</td> +</tr><tr> +<td class="tdl br">Ti</td> +<td class="tdc br">6.5</td> +<td class="tdc br">0.84</td> +<td class="tdl br">\(K_2\)</td> +<td class="tdc br">3500</td> +<td class="tdc br">\(\overline{7}.8\)</td> +<td class="tdc br">2.7</td> +<td class="tdc">\(\overline{8}.5\)</td> +</tr><tr> +<td class="tdl br">Cr</td> +<td class="tdc br">6.75</td> +<td class="tdc br">0.94</td> +<td class="tdl br">\(K_5\)</td> +<td class="tdc br">3000</td> +<td class="tdc br">\(\overline{9}.75\)</td> +<td class="tdc br">2.39</td> +<td class="tdc">\(\overline{10}.1\)</td> +</tr><tr> +<td class="tdl br">Mn</td> +<td class="tdc br">7.41</td> +<td class="tdc br">2.16</td> +<td class="tdl br">\(K_2\)</td> +<td class="tdc br">3500</td> +<td class="tdc br">\(\overline{8}.69\)</td> +<td class="tdc br">3.77</td> +<td class="tdc">\(\overline{10}.4\)</td> +</tr><tr> +<td class="tdl br">Zn</td> +<td class="tdc br">9.35</td> +<td class="tdc br">4.01</td> +<td class="tdl br">\(G_0\)</td> +<td class="tdc br">5600</td> +<td class="tdc br">\(\overline{7}.8\)</td> +<td class="tdc br">3.0</td> +<td class="tdc">\(\overline{10}.8\)</td> +</tr><tr> +<td class="tdl br">Ca+</td> +<td class="tdc br">11.82</td> +<td class="tdc br">0.00</td> +<td class="tdl br">\(K_0\)</td> +<td class="tdc br">4000</td> +<td class="tdc br">\(\overline{9}.46\)</td> +<td class="tdc br">0.00</td> +<td class="tdc">\(\overline{9}.5\)</td> +</tr><tr> +<td class="tdl br">Sr+</td> +<td class="tdc br">10.98</td> +<td class="tdc br">0.00</td> +<td class="tdl br">\(K_2\)</td> +<td class="tdc br">3500</td> +<td class="tdc br">\(\overline{10}.60\)</td> +<td class="tdc br">0.00</td> +<td class="tdc">\(\overline{10}.6\)</td> +</tr><tr> +<td class="tdl br">Ba+</td> +<td class="tdc br">9.96</td> +<td class="tdc br">0.00</td> +<td class="tdl br">\(M_a\)?</td> +<td class="tdc br">3000</td> +<td class="tdc br">\(\overline{11}.89\)</td> +<td class="tdc br">0.00</td> +<td class="tdc">\(\overline{11}.9\)</td> +</tr><tr> +<td class="tdl bb br">Mg</td> +<td class="tdc bb br">7.61</td> +<td class="tdc bb br">2.67</td> +<td class="tdc bb br">\(K_0\)?</td> +<td class="tdc bb br">4000</td> +<td class="tdc bb br">\(\bar{7}.25\)</td> +<td class="tdc bb br">3.25</td> +<td class="tdc bb">\(\overline{10}.5\)</td> +</tr> + </tbody> +</table> + +<p class="nind"> +[<a id="iv">iv</a>: The Schwarzschild approximation to the boundary temperature is +given by the expression +\[ +T_1^{4} = \frac{1}{2} T_0^{4} +\] +<span class="pagenum" id="Page_138">[Pg 138]</span> +where \(T_0\) is the effective temperature and \(T_1\) the boundary +temperature.]</p> + +<p class="nind"> +Successive columns give the atom, the critical potentials in volts, the +spectral class at which maximum occurs, the assumed \(T_{max}\), +\(\log P_e\) calculated from the theory, \(\log n_{r(max)}\), and the +sum of the quantities in the two preceding columns. The only quantity +that is not fixed by the laboratory data is \(T_{max}\), which is +derived from the data presented in <a href="#CHAPTER_II">Chapter II</a>. It will be seen that the +quantity entered in the last column is sensibly constant, and equal to +about -10, in accordance with prediction. All available maxima have +been used.</p> + +<p>It appears that the foregoing evidence constitutes a fair and +satisfactory test of the Fowler-Milne equations, and that, in +the region in which the test can be applied, the agreement with +theory is as close as can be expected from the material. It also +appears that the “serious and undoubtedly real” discordance +of theory and observation, quoted by Menzel in the discussion +of the maxima observed by him, is removed by introducing these +considerations of level.</p> + +<p>When the theory has been applied and justified for the classes where +the temperature scale is well determined by other methods, it may be +extrapolated to fix the temperature scale for the hotter stars. As +before, the fractional concentration at maximum varies but slowly with +\(T\), and \(T_{max}\) is determined mainly by \(P_e\). If now \(P_e\) +be so chosen that \(P_e~ \times~n_{r(max)}\) is always approximately +equal to \(10^{-10}\), the value of \(T\) derived from the equations +will be the appropriate one for the class in question. This value of +\(T\) has to be found by trial. It so happens that the temperatures +thus obtained are not very different from those originally predicted +without entering into considerations of effective level. The excitation +potentials of the highly ionized stages of the lighter elements are +invariably large, and all lead to values of \(P_e\) of the order of +\(10^{-4}\). It is to be noted that values of \(P_e\) <i>greater</i> +than \(10^{-4}\) are not indicated.</p> + +<p>The following tabulation represents the resulting temperature scale for +<span class="pagenum" id="Page_139">[Pg 139]</span> +the hotter stars. It must be remembered that \(T_{max}\) is here the +<i>derived</i> quantity, whereas in <a href="#TABLE_XX">Table XX</a> it was the known quantity +used for calibration.</p> + +<h2><a id="TABLE_XXI">TABLE XXI</a></h2> + +<table class="autotable"> +<thead><tr> +<th class="tdc bb bt2 br">Atom </th> +<th class="tdc_ws1 bb bt2 br"> Ionization<br> +Potential </th> +<th class="tdc_ws1 bb bt2 br"> Excitation<br> +Potential </th> +<th class="tdc bb bt2 br"> Max. </th> +<th class="tdc bb bt2"> \(T_{max}\) </th> +</tr> +</thead> +<tbody><tr> +<td class="tdl br">He+</td> +<td class="tdc br">54.2</td> +<td class="tdc br">48.2</td> +<td class="tdc br">\(O\)</td> +<td class="tdc">35000°</td> +</tr><tr> +<td class="tdl br">C+</td> +<td class="tdc br">24.3</td> +<td class="tdc br">18.0</td> +<td class="tdc br">\(B_3\)</td> +<td class="tdc">l6000</td> +</tr><tr> +<td class="tdl br">He</td> +<td class="tdc br">24.7</td> +<td class="tdc br">21.1</td> +<td class="tdc br">\(B_3\)</td> +<td class="tdc">10000</td> +</tr><tr> +<td class="tdl br">Si++</td> +<td class="tdc br">31.7</td> +<td class="tdc br">4.8</td> +<td class="tdc br">\(B_2-B_1\)</td> +<td class="tdc">18000</td> +</tr><tr> +<td class="tdl bb br">Si+++</td> +<td class="tdc bb br">45.0</td> +<td class="tdc bb br">24.0</td> +<td class="tdc bb br">\(O\)</td> +<td class="tdc bb">25000</td> +</tr> + </tbody> +</table> + + +<p>The values given in the preceding table constitute the only +contribution that can be made by this form of ionization theory to +the formation of a stellar temperature scale. Values assigned to +intermediate classes must be conjectural. From the observed changes +of intensity from class to class, temperatures may be interpolated +roughly, and a temperature scale, formed on these general grounds, is +reproduced in <a href="#TABLE_XXII">Table XXII</a>. Values not derived from observed maxima are +italicized.</p> + +<h2><a id="TABLE_XXII">TABLE XXII</a></h2> + +<table class="autotable"> +<thead><tr> +<th class="tdc">Class </th> +<th class="tdc">Temperature</th> +<th class="tdc"> </th> +<th class="tdc">Class</th> +<th class="tdc">Temperature</th> +</tr> +</thead> +<tbody><tr> +<td class="tdl">\(M_a\)</td> +<td class="tdc">3000°</td> +<td class="tdc"></td> +<td class="tdc">\(A_3\)</td> +<td class="tdc">9000°</td> +</tr><tr> +<td class="tdl">\(K_5\)</td> +<td class="tdc">3000</td> +<td class="tdc"></td> +<td class="tdc">\(A_0\)</td> +<td class="tdc">10000</td> +</tr><tr> +<td class="tdl">\(K_2\)</td> +<td class="tdc">3500</td> +<td class="tdc"></td> +<td class="tdc">\(B_8\)</td> +<td class="tdc">13500</td> +</tr><tr> +<td class="tdl">\(K_0\)</td> +<td class="tdc">4000</td> +<td class="tdc"></td> +<td class="tdc">\(B_5\)</td> +<td class="tdc"><i>15000</i></td> +</tr><tr> +<td class="tdl">\(G_5\)</td> +<td class="tdc"><i>5000</i></td> +<td class="tdc"></td> +<td class="tdc">\(B_3\)</td> +<td class="tdc">17000</td> +</tr><tr> +<td class="tdl">\(G_0\)</td> +<td class="tdc">5600</td> +<td class="tdc"></td> +<td class="tdc">\(B_{1.5}\)</td> +<td class="tdc">18000</td> +</tr><tr> +<td class="tdl">\(F_5\)</td> +<td class="tdc"><i>7000</i></td> +<td class="tdc"></td> +<td class="tdc">\(B_0\)</td> +<td class="tdc"><i>20000</i></td> +</tr><tr> +<td class="tdl">\(F_0\)</td> +<td class="tdc"><i>7500</i></td> +<td class="tdc"></td> +<td class="tdc">\(O\)</td> +<td class="tdc">25000</td> +</tr><tr> +<td class="tdl">\(A_5\)</td> +<td class="tdc"><i>8400</i></td> +<td class="tdc"></td> +<td class="tdc">to</td> +<td class="tdc">35000</td> +</tr> + </tbody> +</table> + + +<div class="footnotes"><h3>FOOTNOTES:</h3> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_408" href="#FNanchor_408" class="label">[408]</a> +H. C. 258, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_409" href="#FNanchor_409" class="label">[409]</a> +M. N. R. A. S., 84, 499, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_410" href="#FNanchor_410" class="label">[410]</a> +M. N. R. A. S., 84, 499, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_411" href="#FNanchor_411" class="label">[411]</a> +Chapter XIII, <a href="#Page_177">p. 177</a>.</p> + +</div> +</div> + +<hr class="chap x-ebookmaker-drop"> + +<div class="chapter"> +<p><span class="pagenum" id="Page_140">[Pg 140]</span></p> + +<h2 class="nobreak" id="CHAPTER_X">CHAPTER X<br> +EFFECTS OF ABSOLUTE MAGNITUDE UPON +THE SPECTRUM</h2> +</div> + + +<p class="nind"> +DIFFERENCES between the spectra of stars of the same spectral class +have long been recognized. The empirical correlation of relative +line intensities with absolute magnitude was made the basis for the +estimation of spectroscopic parallaxes.<a id="FNanchor_412" href="#Footnote_412" class="fnanchor">[412]</a> Such differences within +a class were later related in a qualitative way to differences of +pressure, in conjunction with the theory of thermal ionization, and +have been regarded as corroborative evidence that the type of process +contemplated by that theory actually represents what goes on in the +atmospheres of the stars.</p> + +<p>In the present chapter the theory of the various effects will first be +discussed, and later the predictions from the theory will be compared +with observational data.</p> + + +<p class="nindc space-above2"> +INFLUENCE OF SURFACE GRAVITY ON THE SPECTRUM</p> + + +<p>The first theoretical discussion of the effects of absolute magnitude +upon the stellar spectrum seems to have been made by Pannekoek,<a id="FNanchor_413" href="#Footnote_413" class="fnanchor">[413]</a> +who pointed out that “stars of the same spectral class ... will show +differences depending solely on ... \(g/k\),” where \(g\) is the +surface gravity, and \(k\) the absorption coefficient. Pannekoek +considered all stars of the same spectral class to have the same +temperature, and for the purposes of his argument the differences +in temperature between giants and dwarfs can be neglected, although +actually they may for other reasons have a noticeable effect on the +spectrum. If \(k\) be regarded as constant, a plausible assumption for +various reasons,<a id="FNanchor_414" href="#Footnote_414" class="fnanchor">[414]</a> “the physical quantity, directly given by the +spectra used for the determination of spectroscopic parallaxes is the +<span class="pagenum" id="Page_141">[Pg 141]</span> +gravitation at the surface of the star.”<a id="FNanchor_415" href="#Footnote_415" class="fnanchor">[415]</a> The relation between the +surface gravity and the pressure is given by +\[ +p = (g/k) \tau +\] +where \(\tau\) is the “homogeneous depth.” The pressure is then +directly proportional to the surface gravity.</p> + + +<p class="nindc space-above2"> +INFLUENCE OF PRESSURE ON THE SPECTRUM</p> + + +<p>Lowered pressure increases the <i>degree of ionization</i>. The +tendency of the atoms to lose electrons by thermal ionization should +depend solely on their energy supply, and should thus be independent +of the pressure. The total absorbing power of the gas will, however, +depend on the <i>number</i> of suitable atoms that it contains, not +upon their <i>rate</i> of formation. The number of suitable ionized +atoms present at any moment in the atmosphere is a function not only +of the rate at which ionization proceeds, but also of the rate of +recombination. The more readily recombination takes place, the larger +is the number of effective neutral atoms, and the smaller the number +of effective ionized atoms, when a steady state is attained. The rate +of recombination, which depends upon the probability of a suitable +encounter between an ionized atom and a free electron, will increase +with the pressure—more accurately, with the partial pressure of free +electrons.</p> + +<p>The higher the pressure, therefore, the greater the number of neutral +atoms, and the smaller the number of ionized atoms. This argument +explains at once the strength of the neutral (arc) lines in the spectra +of stars of low luminosity (high surface gravity), and the predominance +of ionized (spark) lines for absolutely bright stars (low surface +gravity, resulting chiefly from large radius). Low surface gravity, +then, increases the number of ionized atoms present by discouraging +recombination.</p> + +<p>It should be noted that any tendency to extensive ionization will +increase the concentration of free electrons and tend to encourage +<span class="pagenum" id="Page_142">[Pg 142]</span> +recombination, thus counteracting the effect of low surface gravity. +The effect of an increased concentration of free electrons will not, +however, attain the magnitude of the surface gravity effect, since +even for the hottest stars examined, three electrons appear to be the +largest number that can be thermally removed under reversing layer +conditions.</p> + +<p>The theoretical effect of lowering the pressure has been discussed by +Stewart,<a id="FNanchor_416" href="#Footnote_416" class="fnanchor">[416]</a> who, after alluding to the importance of the surface +gravity, suggested that the ultimate lines of neutral atoms easier to +ionize than the average should be weakened by low pressure, and that +the corresponding enhanced lines should be strengthened. For atoms +harder to ionize than the average the reverse should be the case for +the two classes of lines. From this standpoint he showed that the +absolute magnitude effects might be qualitatively accounted for. The +“average ionization potential” was the average for the lines used in +the estimates; Stewart adopted the value of six volts for Classes \(F\) +to \(K\).</p> + + +<p class="nindc space-above2"> +EFFECT OF TEMPERATURE AND DENSITY GRADIENTS +UPON THE SPECTRUM OF A STAR</p> + + +<p>There is another respect, recently analyzed by Stewart,<a id="FNanchor_417" href="#Footnote_417" class="fnanchor">[417]</a> in which +the spectrum of a giant may be expected to differ from that of the +corresponding dwarf. He points out that “in a giant, owing to the small +density, there is more material overlying the photosphere than in a +dwarf having the same effective temperature; while at the same time +the density in the photospheric region is less in the giant, owing +to the low gravity.” These conditions furnish an interpretation of +the increased blackness and sharpness of the lines in giant stars, as +compared with the corresponding dwarfs. The absorption lines in giants +are <i>blacker</i> because there is more matter above the photosphere +than in dwarfs; they are <i>sharper</i> because the effective level +at which the lines originate is at a lower pressure in the giant than +in the dwarf, owing to the smaller pressure gradient in the giant +<span class="pagenum" id="Page_143">[Pg 143]</span> +star, and to its lower surface gravity. The difference in line quality +between a giant and a dwarf is at once obvious from the spectra, and +this effect renders direct comparisons of estimated line-intensities a +matter of extreme difficulty. It is an effect that must be taken into +account in examining the agreement between the observations and the +theory.</p> + +<p>Stewart’s argument also suggests the answer to an important question +raised by Pannekoek<a id="FNanchor_418" href="#Footnote_418" class="fnanchor">[418]</a> in the course of his discussion of the +absolute magnitude effect. The latter remarks that “the general +decrease of luminosity with advancing type for the same value of +relative line-intensity, which is shown ... by most reduction curves +... corresponds to the decrease in \(\sigma\), as for the same \(g\) +and smaller \(R\) smaller surface brightness means smaller luminosity. +If we take account, however, of the direct influence of temperature on +ionization, which acts much more strongly in the opposite direction, +we must expect equal ionization in the more advanced types for much +smaller g and higher luminosities, contrary to the empirical reduction +curves. It looks as if this effect is compensated by some other direct +influence of temperature on the spectrum.”<a id="FNanchor_419" href="#Footnote_419" class="fnanchor">[419]</a></p> + +<p>The influence suspected by Pannekoek may be found, at least in +part, in the “theoretical decrease with increasing temperature and +density in the quantity of material overlying the photosphere. Thus +the contrast between line and continuous background tends to become +less along the giant series \(M-B\) (since, furthermore, for the +same abundance of active material, a given line is formed always at +the same depth).”<a id="FNanchor_420" href="#Footnote_420" class="fnanchor">[420]</a> This suggestion was advanced by Stewart to +account for the observed displacement, towards cooler classes, of the +maxima of absorption lines discussed in <a href="#CHAPTER_X">Chapter X</a>. It is certain that +some such factor will be operative in the reversing layer, but it is +believed that the burden of the shift of maxima should be borne by +the effective level, which has been discussed in more detail in the +<span class="pagenum" id="Page_144">[Pg 144]</span> +preceding chapter. It would be of interest to compare the two effects +quantitatively, but the effect of temperature gradient has not yet +formed the basis of numerical predictions.</p> + + +<p class="nindc space-above2"> +PREDICTED EFFECTS ON INDIVIDUAL LINES</p> + + +<p>The discussion involving the average ionization potential appears to +permit of more rigorous treatment. Suppose the “average ionization +potential” of Stewart’s discussion to be replaced by the ionization +potential corresponding to the atoms whose lines are at maximum for +the class in question. It then follows directly from theory that the +effects of lowered pressure on the different classes of lines will be +as below:</p> + +<table class="autotable"> +<thead><tr> +<th class="tdc_bot" rowspan="3">Atom </th> +<th class="tdc_bot" rowspan="3">Line</th> +<th class="tdc" colspan="2">Effect of lowered pressure</th> +</tr><tr> +<th class="tdc">Hotter than class +</th> +<th class="tdc">Cooler than class +</th> +</tr> +<tr> +<th class="tdc">for maximum +</th> +<th class="tdc">for maximum +</th> +</tr> +</thead> +<tbody><tr> +<td class="tdl">Neutral</td> +<td class="tdl">Ultimate</td> +<td class="tdl">Weakened</td> +<td class="tdl">....</td> +</tr><tr> +<td class="tdl">Neutral</td> +<td class="tdl">Subordinate</td> +<td class="tdl">Weakened</td> +<td class="tdl">Weakened</td> +</tr><tr> +<td class="tdl">Ionized</td> +<td class="tdl">Ultimate</td> +<td class="tdl">Weakened</td> +<td class="tdl">Strengthened</td> +</tr><tr> +<td class="tdl">Ionized</td> +<td class="tdl">Subordinate</td> +<td class="tdl">Weakened</td> +<td class="tdl">Strengthened</td> +</tr> + </tbody> +</table> + +<p>It is especially to be noted that all lines should theoretically be +weakened in passing from dwarf to giant, excepting the lines of an +ionized atom at temperatures lower than those required to bring them to +maximum. This leaves out of account the effect of photospheric depth, +which will be introduced later as a correcting factor.</p> + +<p>The case of the ultimate lines of the ionized atoms is of especial +interest. At their maximum, if the Fowler-Milne theory is correct, +ionization is almost complete, and more than 99 per cent of the +element is giving the ionized ultimate lines. At a temperature higher +than that required for maximum, lowered pressure can “increase” the +ionization only by the removal of the second electron. By this process +the intensity of the ionized ultimate lines is decreased, since the +number of singly ionized atoms is thereby reduced. The fall from +maximum towards the hotter stars, which is displayed by the ionized +lines of Ca+, Sr+, and Ba+ can be due only to the progress of second +ionization, and there seems to be no escape from the conclusion that +<span class="pagenum" id="Page_145">[Pg 145]</span> +the ultimate lines of the ionized atom should theoretically decrease in +strength, with lowered pressure, for stars hotter than those required +to bring the lines to maximum. The point is made increasingly clear +when it is recalled that, at the maximum, all of the substance is +presumably at work giving the lines in question. It is not therefore +possible to increase the number of active atoms by any process whatever +that involves merely a change in pressure.</p> + +<p>For ionized subordinate lines the theoretical effect should be the +same as for the ultimate lines, for the fall after maximum is here +again caused by the increase in the number of doubly ionized atoms, and +the consequent decrease in the number of those singly ionized. Thus, +although the subordinate lines are not already using all the available +atoms at maximum, so that increased intensity with lowered pressure +is possible, it would still appear that they should be weakened at +temperatures higher than that corresponding to maximum intensity in the +spectral sequence.</p> + +<p>The pure pressure effects just discussed will be superposed upon the +Stewart effect, which depends upon the photospheric depth. The latter +will cause a general increase in the strength of all lines from dwarf +to giant, as a result of the greater amount of matter lying above the +photosphere in the giant. The two effects are observed together when +direct intensity measures are employed, such as the estimates embodied +in <a href="#CHAPTER_VIII">Chapter VIII</a>, while the pressure effect is given almost purely when +differential estimates of intensity for the same spectrum are used, as +in most investigations of spectroscopic parallax. The observational +evidence from both sources will now be put forward, in order to examine +the sufficiency of the theories that have been advanced to account for +the absolute magnitude effects.</p> + +<p>The empirical relations used in the estimation of spectroscopic +parallax should provide material for examining the simple pressure +effect, as they are derived from the ratio of two lines in the same +spectrum. Unfortunately the line ratios actually in use were selected +<span class="pagenum" id="Page_146">[Pg 146]</span> +because they were convenient to measure, and gave (empirically) +consistent results, not for reasons of theoretical tractability. +Fourteen line ratios are used, for example, by Harper and Young,<a id="FNanchor_421" href="#Footnote_421" class="fnanchor">[421]</a> +but only four of these consist of pairs of unblended lines with known +series relations. It is only for such lines that a useful test of +theory can be made.</p> + +<h2><a id="TABLE_XXIII">TABLE XXIII</a></h2> +<table class="autotable"> +<thead><tr> +<th class="tdc"></th> +<th class="tdc"></th> +<th class="tdc">\(\dfrac{4071}{4077}\)</th> +<th class="tdc">\(F_0\)</th> +<th class="tdc">\(F_5\)</th> +<th class="tdc">\(G_0\)</th> +<th class="tdc">\(G_5\)</th> +<th class="tdc">\(K_0\)</th> +<th class="tdc">\(K_5\)</th> +<th class="tdc">\(M_0\)</th> +<th class="tdc">\(M_5\)</th> +</tr> +</thead> +<tbody><tr> +<td class="tdl">M</td> +<td class="tdc">=</td> +<td class="tdc">+7</td> +<td class="tdc">+8.8</td> +<td class="tdc">+9.2</td> +<td class="tdc">+11.0</td> +<td class="tdc">+13.2</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"></td> +<td class="tdc">+6</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc">+13.3</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"></td> +<td class="tdc">+5</td> +<td class="tdc">+3.5</td> +<td class="tdc">+5.0</td> +<td class="tdc">+7.4</td> +<td class="tdc">+9.6</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"></td> +<td class="tdc">+4</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc">+10.0</td> +<td class="tdc">+10.8</td> +<td class="tdc"></td> +<td class="tdc"></td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"></td> +<td class="tdc">+3</td> +<td class="tdc">-1.8</td> +<td class="tdc">+0.5</td> +<td class="tdc">+3.8</td> +<td class="tdc">+6.7</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"></td> +<td class="tdc">+2</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc">+6.7</td> +<td class="tdc">+7.0</td> +<td class="tdc">+7.6</td> +<td class="tdc">+10.0</td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"></td> +<td class="tdc">+1</td> +<td class="tdc">-7.2</td> +<td class="tdc">-3.8</td> +<td class="tdc">+0.2</td> +<td class="tdc">+3.2</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"></td> +<td class="tdc">0</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc">+3.5</td> +<td class="tdc">+3.4</td> +<td class="tdc">+3.2</td> +<td class="tdc">+3.0</td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"></td> +<td class="tdc">1</td> +<td class="tdc">-12.9</td> +<td class="tdc">-8.2</td> +<td class="tdc">-3.2</td> +<td class="tdc">-0.3</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"></td> +<td class="tdc">-2</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc">+0.3</td> +<td class="tdc">-0.2</td> +<td class="tdc">-1.4</td> +<td class="tdc">-3.7</td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"></td> +<td class="tdc">-3</td> +<td class="tdc"></td> +<td class="tdc">-12.1</td> +<td class="tdc">-7.3</td> +<td class="tdc">-3.8</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"></td> +<td class="tdc">-4</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc">-2.8</td> +<td class="tdc">-4.2</td> +<td class="tdc">-5.8</td> +<td class="tdc">-10.0</td> +</tr> + </tbody> +</table> + +<table class="autotable"> +<thead><tr> +<th class="tdc"></th> +<th class="tdc"></th> +<th class="tdc">\(\dfrac{4215}{4250}\)</th> +<th class="tdc">\(F_0\)</th> +<th class="tdc">\(F_5\)</th> +<th class="tdc">\(G_0\)</th> +<th class="tdc">\(G_5\)</th> +<th class="tdc">\(K_0\)</th> +<th class="tdc">\(K_5\)</th> +<th class="tdc"></th> +<th class="tdc"></th> +</tr> +</thead> +<tbody><tr> +<td class="tdl">M</td> +<td class="tdc">=</td> +<td class="tdc">+6</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc">-2.0</td> +<td class="tdc">-1.4</td> +<td class="tdc"></td> +<td class="tdc"></td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"></td> +<td class="tdc">+5</td> +<td class="tdc">-1.5</td> +<td class="tdc">-0.5</td> +<td class="tdc">0.0</td> +<td class="tdc">+1.0</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"></td> +<td class="tdc">+4</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc">+1.2</td> +<td class="tdc">+1.3</td> +<td class="tdc"></td> +<td class="tdc"></td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"></td> +<td class="tdc">+3</td> +<td class="tdc">+1.8</td> +<td class="tdc">+3.3</td> +<td class="tdc">+4.4</td> +<td class="tdc">+4.5</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"></td> +<td class="tdc">+2</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc">+5.0</td> +<td class="tdc">+3.0</td> +<td class="tdc"></td> +<td class="tdc"></td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"></td> +<td class="tdc">+1</td> +<td class="tdc">+4.8</td> +<td class="tdc">+6.5</td> +<td class="tdc">+7.8</td> +<td class="tdc">+7.6</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"></td> +<td class="tdc">0</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc">+6.5</td> +<td class="tdc">+4.7</td> +<td class="tdc"></td> +<td class="tdc"></td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"></td> +<td class="tdc">-1</td> +<td class="tdc">+8.6</td> +<td class="tdc">+9.3</td> +<td class="tdc">+11.0</td> +<td class="tdc">+11.0</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"></td> +<td class="tdc">-2</td> +<td class="tdc">+12.0</td> +<td class="tdc">+8.6</td> +<td class="tdc">+8.6</td> +<td class="tdc">+8.2</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +</tr> + </tbody> +</table> + +<table class="autotable"> +<thead><tr> +<th class="tdc"></th> +<th class="tdc"></th> +<th class="tdc">\(\dfrac{4247}{4250}\)</th> +<th class="tdc">\(F_0\)</th> +<th class="tdc">\(F_5\)</th> +<th class="tdc">\(G_0\)</th> +<th class="tdc">\(G_5\)</th> +<th class="tdc">\(K_0\)</th> +<th class="tdc"></th> +<th class="tdc"></th> +<th class="tdc"></th> +</tr> +</thead> +<tbody><tr> +<td class="tdl">M</td> +<td class="tdc">=</td> +<td class="tdc">+6</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc">-18.1</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"></td> +<td class="tdc">+5</td> +<td class="tdc">-3.7</td> +<td class="tdc">-5.8</td> +<td class="tdc">-9.6</td> +<td class="tdc">-14.7</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"></td> +<td class="tdc">+4</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc">-15.3</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"></td> +<td class="tdc">+3</td> +<td class="tdc">-1.0</td> +<td class="tdc">-3.3</td> +<td class="tdc">-6.6</td> +<td class="tdc">-11.0</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"></td> +<td class="tdc">+2</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc">-12.4</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"></td> +<td class="tdc">+1</td> +<td class="tdc">+1.7</td> +<td class="tdc">-0.6</td> +<td class="tdc">-3.7</td> +<td class="tdc">-7.5</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"></td> +<td class="tdc">0</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc">-9.4</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"></td> +<td class="tdc">-1</td> +<td class="tdc">+4.5</td> +<td class="tdc">+2.0</td> +<td class="tdc">-0.9</td> +<td class="tdc">-4.0</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"></td> +<td class="tdc">-2</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc">-6.6</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"></td> +<td class="tdc">-3</td> +<td class="tdc">+7.2</td> +<td class="tdc">+4.7</td> +<td class="tdc">+2.0</td> +<td class="tdc">-0.2</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +</tr> + </tbody> +</table> + +<table class="autotable"> +<thead><tr> +<th class="tdc"></th> +<th class="tdc"></th> +<th class="tdc">\(\dfrac{4455}{4404}\)</th> +<th class="tdc"></th> +<th class="tdc"></th> +<th class="tdc"></th> +<th class="tdc">\(G_5\)</th> +<th class="tdc">\(K_0\)</th> +<th class="tdc">\(K_5\)</th> +<th class="tdc"></th> +<th class="tdc"></th> +</tr> +</thead> +<tbody><tr> +<td class="tdl">M</td> +<td class="tdc">=</td> +<td class="tdc">+6</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc">+7.4</td> +<td class="tdc">+6.2</td> +<td class="tdc"></td> +<td class="tdc"></td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"></td> +<td class="tdc">+5</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc">+6.2</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"></td> +<td class="tdc">+4</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc">+4.3</td> +<td class="tdc">+3.0</td> +<td class="tdc"></td> +<td class="tdc"></td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"></td> +<td class="tdc">+3</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc">+3.0</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"></td> +<td class="tdc">+2</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc">+1.3</td> +<td class="tdc">0.0</td> +<td class="tdc"></td> +<td class="tdc"></td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"></td> +<td class="tdc">+1</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc">0.0</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"></td> +<td class="tdc">0</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc">0.0</td> +<td class="tdc">-2.0</td> +<td class="tdc"></td> +<td class="tdc"></td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"></td> +<td class="tdc">1</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc">+2.6</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"></td> +<td class="tdc">-2</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc">+2.0</td> +<td class="tdc">+0.7</td> +<td class="tdc"></td> +<td class="tdc"></td> +</tr><tr> +<td class="tdl"></td> +<td class="tdc"></td> +<td class="tdc">-3</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc">+5.2</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +</tr> + </tbody> +</table> + +<p><span class="pagenum" id="Page_147">[Pg 147]</span></p> + +<p>The preceding table contains a transcription of the reduction-curve +material given by Harper and Young for the four pairs of lines +mentioned. Tabulated quantities are the “step differences” for the +classes at the heads of the columns, and the absolute magnitudes +contained in the first column.</p> + +<p>Presumably the irregularities of the observed curves have been smoothed +out in forming the reduction table, but the figures will certainly give +an indication of the direction in which a given line is affected by +absolute magnitude.</p> + +<p>The predicted effect of lowered pressure upon the lines involved is +contained in the table that follows:</p> + +<table class="autotable"> +<thead><tr> +<th class="tdc">Line </th> +<th class="tdc"> Source </th> +<th class="tdc"> Max. </th> +<th class="tdc">Effect of lowered pressure</th> +</tr> +</thead> +<tbody><tr> +<td class="tdc">4071</td> +<td class="tdc">Fe (sub)</td> +<td class="tdc">\(K_2\)</td> +<td class="tdl">weakened throughout</td> +</tr><tr> +<td class="tdc">4077</td> +<td class="tdc">Sr+ (ult)</td> +<td class="tdc">\(K_2\)</td> +<td class="tdl">strengthened in \(M\), weakened in \(G\) and \(F\)</td> +</tr><tr> +<td class="tdc">4215</td> +<td class="tdc">Sr+ (ult)</td> +<td class="tdc">\(K_2\)</td> +<td class="tdl">strengthened in \(M\), weakened in \(G\) and \(F\)</td> +</tr><tr> +<td class="tdc">4247</td> +<td class="tdc">Sc+ (?)</td> +<td class="tdc">\(F_0\)</td> +<td class="tdl">strengthened throughout range</td> +</tr><tr> +<td class="tdc">4250</td> +<td class="tdc">Fe (sub)</td> +<td class="tdc">\(K_2\)</td> +<td class="tdl">weakened throughout</td> +</tr><tr> +<td class="tdc">4455</td> +<td class="tdc">Ca (sub)</td> +<td class="tdc">\(M_a\)</td> +<td class="tdl">weakened throughout</td> +</tr><tr> +<td class="tdc">4494</td> +<td class="tdc">Fe (sub)</td> +<td class="tdc">\(K_2\)</td> +<td class="tdl">weakened throughout</td> +</tr> + </tbody> +</table> + + +<p>The predicted changes in the line ratios with lowered pressure are +therefore as follows: +\[ +\begin{array}{l} +\frac{4071}{4077}~~\text{increased from}\,\, F_0\, \text{to}\,\, K_0, \text{decreased from}\, M_0\, \text{to}\,\, M_5\\ +\frac{4215}{4250}~~\text{increased from}\,\, F_0\, \text{to}\,\, K_0, \text{decreased from}\,\, M_0\, \text{to}\,\, M_5\\ +\frac{4247}{4250}~~\text{increased throughout}\\ +\frac{4455}{4494}~~\text{indeterminate}\\ +\end{array} +\]</p> + +<p>The ratio \(\dfrac{4247}{4250}\) behaves in exact accordance with +prediction, and \(\dfrac{4455}{4494}\) which decreases and then +increases again, offers no evidence for or against the theory. The +two remaining ratios, involving the two Sr+ lines, display a lack of +agreement with theory for the \(F\) and \(G\) classes, apparently +owing to the strengthening of the Sr+ lines with high luminosity, +even at temperatures higher than those at which they attain maximum +<span class="pagenum" id="Page_148">[Pg 148]</span> +intensity. The strengthening of Sr+ with high luminosity is one of +the best-attested facts of observational astrophysics, and it is a +serious deficiency in theory if the observed behavior of the lines in +the hotter stars cannot be explained. The question will be further +discussed presently.</p> + +<p>The material obtained by the writer, and summarized in a preceding +chapter,<a id="FNanchor_422" href="#Footnote_422" class="fnanchor">[422]</a> may be used in making a test of the predicted pressure +effects by means of direct estimates. As was pointed out above, the +lines of a giant are stronger than those of a dwarf, owing to the +greater photospheric depth in the former. The practical difficulty of +making comparable estimates upon sharp and somewhat hazy lines must +also be considered in the discussion of the results. Clearly some +numerical correction is required, in order to allow for the Stewart +effect, and this has been done in a somewhat arbitrary manner in +forming <a href="#TABLE_XXIV">Table XXIV</a>. It is assumed that the mean increase in intensity +for such lines as are strengthened will be equal to the mean decrease +in intensity for such lines as are weakened. For each spectral class +this assumption provides a correcting factor, which never exceeds one +scale unit.</p> + +<p>The table that follows contains the material derived from the measures +enumerated in <a href="#CHAPTER_VIII">Chapter VIII</a>, and from other sources, bearing on the +intensity differences between giants and dwarfs of the same spectral +class. All the available estimates have been used. Successive columns +give the line, the atom, the predicted behavior, and the observed +difference in the sense giant-dwarf, for the Classes \(F_0\), \(F_2\), +\(F_5\), \(F_8\), \(G_0\), and \(G_5\). The symbols \(u\), \(n\), and +\(*\), following the atom, denote ultimate, neutral, and enhanced +lines, respectively. The number of stars contributing to each entry +will be seen from the list on <a href="#Page_119">p. 119</a>, Chapter VIII. The notation is as +follows: 0 = no change; ± 0 = between 0 and 1; ± 1 = between 1 and 2; ± +2 = between 2 and 3; and so on. The values for \(K_0\) are taken from +Menzel’s measures<a id="FNanchor_423" href="#Footnote_423" class="fnanchor">[423]</a> of \(\epsilon\) Indi and \(\alpha\) Tauri, “the +scale of intensities being (0) no difference, (1) a little stronger +<span class="pagenum" id="Page_149">[Pg 149]</span> +(2) much stronger, (3) very much stronger.” The signs from Menzel’s +table are reversed, in accordance with the notation used in the +present table. In the column headed \(M_a\) are the signs indicating +the direction in which the corresponding lines are affected in that +class,<a id="FNanchor_424" href="#Footnote_424" class="fnanchor">[424]</a> for which quantitative measures have not been published. +The letters “\(s\)” and “\(w\)” in the column headed \(G_0\) refer to +strengthening or weakening of lines, as observed by Baxandall<a id="FNanchor_425" href="#Footnote_425" class="fnanchor">[425]</a> in +a comparison of the solar spectrum with that of Capella. Baxandall’s +estimates are inserted to supplement the present material. The numerous +gaps in the table result from the difficulty of seeing the fainter +lines in the dwarf spectrum.</p> + +<h2><a id="TABLE_XXIV">TABLE XXIV</a></h2> + +<table class="autotable"> +<thead><tr> +<th class="tdc bt2 bb br" rowspan="2">Line</th> +<th class="tdc bt2 bb br" rowspan="2" colspan="2">Element</th> +<th class="tdc bt2 br" colspan="3">Predicted Effect</th> +<th class="tdc bt2" colspan="7">Observed Effect</th> +</tr> +<tr> +<th class="tdc bb">-</th> +<th class="tdc bb">0</th> +<th class="tdc bb br">+</th> +<th class="tdc bb">\(F_0\)</th> +<th class="tdc bb">\(F_2\)</th> +<th class="tdc bb">\(F_5\)</th> +<th class="tdc bb">\(G_0\)</th> +<th class="tdc bb">\(G_5\)</th> +<th class="tdc bb">\(K_0\)</th> +<th class="tdc bb">\(M_a\)</th> +</tr> +</thead> +<tbody><tr> +<td class="tdc br">3933</td> +<td class="tdl">Ca+</td> +<td class="tdr br">*</td> +<td class="tdc">\(F_0-G_5\)</td> +<td class="tdc">\(K_0\)</td> +<td class="tdc br">\(M_a\)</td> +<td class="tdc">+1</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">0?</td> +<td class="tdc">+</td> +</tr><tr> +<td class="tdc br">3944</td> +<td class="tdl">Al</td> +<td class="tdr br">u</td> +<td class="tdc">\(F_0-M_a\)</td> +<td class="tdc">..</td> +<td class="tdc br">..</td> +<td class="tdc">+0</td> +<td class="tdc">+</td> +<td class="tdc">-2</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">-</td> +</tr><tr> +<td class="tdc br">3953</td> +<td class="tdl">Fe</td> +<td class="tdc br">n</td> +<td class="tdc">\(F_0-K_0\)</td> +<td class="tdc">(\(K_2\))</td> +<td class="tdc br">..</td> +<td class="tdc">+0</td> +<td class="tdc">+</td> +<td class="tdc">-2</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +</tr><tr> +<td class="tdc br">3961</td> +<td class="tdl">Al</td> +<td class="tdr br">u</td> +<td class="tdc">\(F_0-M_a\)</td> +<td class="tdc">..</td> +<td class="tdc br">..</td> +<td class="tdc">+0</td> +<td class="tdc">+</td> +<td class="tdc">-2</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">-</td> +</tr><tr> +<td class="tdc br">3968</td> +<td class="tdl">Ca+</td> +<td class="tdr br">*</td> +<td class="tdc">\(F_0-G_5\)</td> +<td class="tdc">\(K_0\)</td> +<td class="tdc br">\(M_a\)</td> +<td class="tdc">+1</td> +<td class="tdc">..</td> +<td class="tdc">-1</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">0?</td> +<td class="tdc">+</td> +</tr><tr> +<td class="tdc br">3999</td> +<td class="tdl">Ti</td> +<td class="tdr br">u</td> +<td class="tdc">\(F_0-M_a\)</td> +<td class="tdc">..</td> +<td class="tdc br">..</td> +<td class="tdc">+0</td> +<td class="tdc">..</td> +<td class="tdc">-1</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +</tr><tr> +<td class="tdc br">4005</td> +<td class="tdl">Fe</td> +<td class="tdr br">n</td> +<td class="tdc">\(F_0-M_a\)</td> +<td class="tdc">..</td> +<td class="tdc br">..</td> +<td class="tdc">+0</td> +<td class="tdc">..</td> +<td class="tdc">0</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +</tr><tr> +<td class="tdc br">4031</td> +<td class="tdl">Mn</td> +<td class="tdr br">u</td> +<td class="tdc">\(F_0-M_a\)</td> +<td class="tdc">..</td> +<td class="tdc br">..</td> +<td class="tdc">-2</td> +<td class="tdc">-1</td> +<td class="tdc">-1</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">0</td> +<td class="tdc">..</td> +</tr><tr> +<td class="tdc br">4041</td> +<td class="tdl">Mn</td> +<td class="tdr br">n</td> +<td class="tdc">\(F_0-M_a\)</td> +<td class="tdc">..</td> +<td class="tdc br">..</td> +<td class="tdc">-1</td> +<td class="tdc">-1</td> +<td class="tdc">-2</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">-0</td> +<td class="tdc">..</td> +</tr><tr> +<td class="tdc br">4046</td> +<td class="tdl">Fe</td> +<td class="tdr br">n</td> +<td class="tdc">\(F_0-M_a\)</td> +<td class="tdc">..</td> +<td class="tdc br">..</td> +<td class="tdc">-1</td> +<td class="tdc">-1</td> +<td class="tdc">0</td> +<td class="tdc">-1</td> +<td class="tdc">-1</td> +<td class="tdc">-2</td> +<td class="tdc">..</td> +</tr><tr> +<td class="tdc br">4064</td> +<td class="tdl">Fe</td> +<td class="tdr br">n</td> +<td class="tdc">\(F_0-M_a\)</td> +<td class="tdc">..</td> +<td class="tdc br">..</td> +<td class="tdc">-1</td> +<td class="tdc">-2</td> +<td class="tdc">..</td> +<td class="tdc">+2</td> +<td class="tdc">0</td> +<td class="tdc">-2</td> +<td class="tdc">..</td> +</tr><tr> +<td class="tdc br">4068</td> +<td class="tdl">FeMn</td> +<td class="tdr br">n</td> +<td class="tdc">\(F_0-M_a\)</td> +<td class="tdc">..</td> +<td class="tdc br">..</td> +<td class="tdc">-1</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">+1</td> +<td class="tdc">-1</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +</tr><tr> +<td class="tdc br">4072</td> +<td class="tdl">Fe,-</td> +<td class="tdr br">n</td> +<td class="tdc">\(F_0-M_a\)</td> +<td class="tdc">..</td> +<td class="tdc br">..</td> +<td class="tdc">0</td> +<td class="tdc">+4</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">-1</td> +<td class="tdc">-2</td> +<td class="tdc">..</td> +</tr><tr> +<td class="tdc br">4077</td> +<td class="tdl">Sr+</td> +<td class="tdc br">*</td> +<td class="tdc">\(F_0-K_0\)</td> +<td class="tdc">\(K_2\)</td> +<td class="tdc br">\(K_5-M_a\)</td> +<td class="tdc">0</td> +<td class="tdc">0</td> +<td class="tdc">+1</td> +<td class="tdc">s</td> +<td class="tdc">0</td> +<td class="tdc">+3</td> +<td class="tdc">+</td> +</tr><tr> +<td class="tdc br">4084</td> +<td class="tdl">Fe</td> +<td class="tdr br">n</td> +<td class="tdc">\(F_0-K_0\)</td> +<td class="tdc">..</td> +<td class="tdc br">..</td> +<td class="tdc">-1</td> +<td class="tdc">+1</td> +<td class="tdc">0</td> +<td class="tdc">0</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +</tr><tr> +<td class="tdc br">4101</td> +<td class="tdl">H</td> +<td class="tdr br">n</td> +<td class="tdc">\(F_0-M_a\)</td> +<td class="tdc">..</td> +<td class="tdc br">..</td> +<td class="tdc">-1</td> +<td class="tdc">-1</td> +<td class="tdc">+1</td> +<td class="tdc">-4</td> +<td class="tdc">0</td> +<td class="tdc">-1</td> +<td class="tdc">+</td> +</tr><tr> +<td class="tdc br">4132</td> +<td class="tdl">Fe</td> +<td class="tdr br">n</td> +<td class="tdc">\(F_0-M_a\)</td> +<td class="tdc">..</td> +<td class="tdc br">..</td> +<td class="tdc">0</td> +<td class="tdc">+2</td> +<td class="tdc">+1</td> +<td class="tdc">..</td> +<td class="tdc">+0</td> +<td class="tdc">-1</td> +<td class="tdc">..</td> +</tr><tr> +<td class="tdc br">4135</td> +<td class="tdl">Fe</td> +<td class="tdr br">n</td> +<td class="tdc">\(F_0-M_a\)</td> +<td class="tdc">..</td> +<td class="tdc br">..</td> +<td class="tdc">-1</td> +<td class="tdc">..</td> +<td class="tdc">0</td> +<td class="tdc">..</td> +<td class="tdc">+0</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +</tr><tr> +<td class="tdc br">4144</td> +<td class="tdl">Fe</td> +<td class="tdr br">n</td> +<td class="tdc">\(F_0-M_a\)</td> +<td class="tdc">..</td> +<td class="tdc br">..</td> +<td class="tdc">-1</td> +<td class="tdc">0</td> +<td class="tdc">+2</td> +<td class="tdc">0</td> +<td class="tdc">+0</td> +<td class="tdc">-1</td> +<td class="tdc">..</td> +</tr><tr> +<td class="tdc br">4167</td> +<td class="tdl">?</td> +<td class="tdr br"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc br"></td> +<td class="tdc">-1</td> +<td class="tdc">..</td> +<td class="tdc">-1</td> +<td class="tdc">-1w</td> +<td class="tdc">0</td> +<td class="tdc">..</td> +<td class="tdc">.. +<span class="pagenum" id="Page_150">[Pg 150]</span></td> +</tr><tr> +<td class="tdc br">4172</td> +<td class="tdl">Fe+</td> +<td class="tdr br">*</td> +<td class="tdc"></td> +<td class="tdc">\(F_0\)</td> +<td class="tdc br">\(F_2-M_a\)</td> +<td class="tdc">+1</td> +<td class="tdc">+1</td> +<td class="tdc">+3</td> +<td class="tdc">+1</td> +<td class="tdc">+0</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +</tr><tr> +<td class="tdc br">4177</td> +<td class="tdl">Fe+</td> +<td class="tdr br">*</td> +<td class="tdc"></td> +<td class="tdc">\(F_0\)</td> +<td class="tdc br">\(F_2-M_a\)</td> +<td class="tdc">+1</td> +<td class="tdc">..</td> +<td class="tdc">+2</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +</tr><tr> +<td class="tdc br">4215</td> +<td class="tdl">Sr+</td> +<td class="tdr br">*</td> +<td class="tdc">\(F_0-K_0\)</td> +<td class="tdc">\(K_2\)</td> +<td class="tdc br">\(K_5-M_a\)</td> +<td class="tdc">0</td> +<td class="tdc">0</td> +<td class="tdc">+2</td> +<td class="tdc">+3</td> +<td class="tdc">+0</td> +<td class="tdc">+1</td> +<td class="tdc">+</td> +</tr><tr> +<td class="tdc br">4227</td> +<td class="tdl">Ca</td> +<td class="tdr br">u</td> +<td class="tdc">\(F_0-M_a\)</td> +<td class="tdc">..</td> +<td class="tdc br">..</td> +<td class="tdc">-1</td> +<td class="tdc">-1</td> +<td class="tdc">0</td> +<td class="tdc">-2</td> +<td class="tdc">-0</td> +<td class="tdc">-2</td> +<td class="tdc">-</td> +</tr><tr> +<td class="tdc br">4247</td> +<td class="tdl">Sc+</td> +<td class="tdr br">*</td> +<td class="tdc">..</td> +<td class="tdc">\(F_0\)</td> +<td class="tdc br">\(F_2-M_a\)</td> +<td class="tdc">0</td> +<td class="tdc">..</td> +<td class="tdc">+1</td> +<td class="tdc">..</td> +<td class="tdc">+1</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +</tr><tr> +<td class="tdc br">4250</td> +<td class="tdl">Fe</td> +<td class="tdr br">n</td> +<td class="tdc">\(F_0-M_a\)</td> +<td class="tdc">..</td> +<td class="tdc br">..</td> +<td class="tdc">0</td> +<td class="tdc">-2</td> +<td class="tdc">-1</td> +<td class="tdc">-2</td> +<td class="tdc">-1</td> +<td class="tdc">-2</td> +<td class="tdc">..</td> +</tr><tr> +<td class="tdc br">4254</td> +<td class="tdl">Cr</td> +<td class="tdc br">u</td> +<td class="tdc">\(F_0-M_a\)</td> +<td class="tdc">..</td> +<td class="tdc br">..</td> +<td class="tdc">-1</td> +<td class="tdc">..</td> +<td class="tdc">-1</td> +<td class="tdc">-1</td> +<td class="tdc">-1</td> +<td class="tdc">-1</td> +<td class="tdc">..</td> +</tr><tr> +<td class="tdc br">4260</td> +<td class="tdl">Fe</td> +<td class="tdr br">n</td> +<td class="tdc">\(F_0-M_a\)</td> +<td class="tdc">..</td> +<td class="tdc br">..</td> +<td class="tdc">-1</td> +<td class="tdc">-2</td> +<td class="tdc">-1</td> +<td class="tdc">-2</td> +<td class="tdc">..</td> +<td class="tdc">-1</td> +<td class="tdc">-</td> +</tr><tr> +<td class="tdc br">4272</td> +<td class="tdl">Fe</td> +<td class="tdr br">n</td> +<td class="tdc">\(F_0-M_a\)</td> +<td class="tdc">..</td> +<td class="tdc br">..</td> +<td class="tdc">-1</td> +<td class="tdc">-2</td> +<td class="tdc">..</td> +<td class="tdc">0</td> +<td class="tdc">+0</td> +<td class="tdc">-1</td> +<td class="tdc">..</td> +</tr><tr> +<td class="tdc br">4275</td> +<td class="tdl">Br</td> +<td class="tdr br">u</td> +<td class="tdc">\(F_0-M_a\)</td> +<td class="tdc">..</td> +<td class="tdc br">..</td> +<td class="tdc">-1</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">0</td> +<td class="tdc">+0</td> +<td class="tdc">-1</td> +<td class="tdc">..</td> +</tr><tr> +<td class="tdc br">4290</td> +<td class="tdl">Cr</td> +<td class="tdr br">u</td> +<td class="tdc">\(F_0-M_a\)</td> +<td class="tdc">..</td> +<td class="tdc br">..</td> +<td class="tdc">0</td> +<td class="tdc">-2</td> +<td class="tdc">0</td> +<td class="tdc">..</td> +<td class="tdc">+0</td> +<td class="tdc">-1</td> +<td class="tdc">..</td> +</tr><tr> +<td class="tdc br">4298</td> +<td class="tdl">Ti, Ca</td> +<td class="tdr br"></td> +<td class="tdc">\(F_0-M_a\)</td> +<td class="tdc">..</td> +<td class="tdc br">..</td> +<td class="tdc">-1</td> +<td class="tdc">-2</td> +<td class="tdc">0</td> +<td class="tdc">..</td> +<td class="tdc">0</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +</tr><tr> +<td class="tdc br">4308</td> +<td class="tdl">Fe</td> +<td class="tdr br">n</td> +<td class="tdc">\(F_0-M_a\)</td> +<td class="tdc">..</td> +<td class="tdc br">..</td> +<td class="tdc">0</td> +<td class="tdc">+1</td> +<td class="tdc">0</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">-1</td> +<td class="tdc">..</td> +</tr><tr> +<td class="tdc br">4315</td> +<td class="tdl">Fe+</td> +<td class="tdr br">*</td> +<td class="tdc">..</td> +<td class="tdc">\(F_0\)</td> +<td class="tdc br">\(F_2-M_a\)</td> +<td class="tdc">0</td> +<td class="tdc">+1</td> +<td class="tdc">+2</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +</tr><tr> +<td class="tdc br">4321</td> +<td class="tdl">Sc+</td> +<td class="tdr br">*</td> +<td class="tdc">..</td> +<td class="tdc">\(F_0\)</td> +<td class="tdc br">\(F_2-M_a\)</td> +<td class="tdc">+1</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">s</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +</tr><tr> +<td class="tdc br">4326</td> +<td class="tdl">Fe</td> +<td class="tdr br">n</td> +<td class="tdc">\(F_0-M_a\)</td> +<td class="tdc">..</td> +<td class="tdc br">..</td> +<td class="tdc">0</td> +<td class="tdc">+1</td> +<td class="tdc">+1</td> +<td class="tdc">-2w</td> +<td class="tdc">0</td> +<td class="tdc">-2</td> +<td class="tdc">..</td> +</tr><tr> +<td class="tdc br">4340</td> +<td class="tdl">H</td> +<td class="tdr br">n</td> +<td class="tdc">\(F_0-M_a\)</td> +<td class="tdc">..</td> +<td class="tdc br">..</td> +<td class="tdc">-2</td> +<td class="tdc">-7</td> +<td class="tdc">-1</td> +<td class="tdc">-4</td> +<td class="tdc">-0</td> +<td class="tdc">-1</td> +<td class="tdc">+</td> +</tr><tr> +<td class="tdc br">4352</td> +<td class="tdl">CrMg</td> +<td class="tdc br"></td> +<td class="tdc">\(F_0-M_a\)?</td> +<td class="tdc">..</td> +<td class="tdc br">..</td> +<td class="tdc">0</td> +<td class="tdc">+2</td> +<td class="tdc">0</td> +<td class="tdc">+1</td> +<td class="tdc">+0</td> +<td class="tdc">-3</td> +<td class="tdc">..</td> +</tr><tr> +<td class="tdc br">4360</td> +<td class="tdl">Cr</td> +<td class="tdr br">n</td> +<td class="tdc">\(F_0-M_a\)</td> +<td class="tdc">..</td> +<td class="tdc br">..</td> +<td class="tdc">0</td> +<td class="tdc">..</td> +<td class="tdc">+1</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +</tr><tr> +<td class="tdc br">4370</td> +<td class="tdl">Fe</td> +<td class="tdr br">n</td> +<td class="tdc">\(F_0-M_a\)</td> +<td class="tdc">..</td> +<td class="tdc br">..</td> +<td class="tdc">+1</td> +<td class="tdc">..</td> +<td class="tdc">0</td> +<td class="tdc">..</td> +<td class="tdc">+0</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +</tr><tr> +<td class="tdc br">4376</td> +<td class="tdl">Y+</td> +<td class="tdr br">*</td> +<td class="tdc">..</td> +<td class="tdc">\(F_0\)</td> +<td class="tdc br">\(F_2-M_a\)</td> +<td class="tdc">-1</td> +<td class="tdc">+2</td> +<td class="tdc">0</td> +<td class="tdc">..</td> +<td class="tdc">+1</td> +<td class="tdc">+2</td> +<td class="tdc">..</td> +</tr><tr> +<td class="tdc br">4383</td> +<td class="tdl">Fe</td> +<td class="tdr br">n</td> +<td class="tdc">\(F_0-M_a\)</td> +<td class="tdc">..</td> +<td class="tdc br">..</td> +<td class="tdc">0</td> +<td class="tdc">+3</td> +<td class="tdc">+1</td> +<td class="tdc">-2</td> +<td class="tdc">-4</td> +<td class="tdc">-2</td> +<td class="tdc">..</td> +</tr><tr> +<td class="tdc br">4405</td> +<td class="tdl">Fe</td> +<td class="tdr br">n</td> +<td class="tdc">\(F_0-M_a\)</td> +<td class="tdc">..</td> +<td class="tdc br">..</td> +<td class="tdc">-1</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">0</td> +<td class="tdc">-1</td> +<td class="tdc">-2</td> +<td class="tdc">..</td> +</tr><tr> +<td class="tdc br">4415</td> +<td class="tdl">Fe+</td> +<td class="tdr br">*</td> +<td class="tdc">..</td> +<td class="tdc">\(F_0\)</td> +<td class="tdc br">\(F_2-M_a\)</td> +<td class="tdc">+1</td> +<td class="tdc">0</td> +<td class="tdc">+3</td> +<td class="tdc">0</td> +<td class="tdc">0</td> +<td class="tdc">-1</td> +<td class="tdc">..</td> +</tr><tr> +<td class="tdc br">4435</td> +<td class="tdl">Ca</td> +<td class="tdr br">n</td> +<td class="tdc">\(F_0-M_a\)</td> +<td class="tdc">..</td> +<td class="tdc br">..</td> +<td class="tdc">-1</td> +<td class="tdc">..</td> +<td class="tdc">+1</td> +<td class="tdc">..</td> +<td class="tdc">0</td> +<td class="tdc">-2</td> +<td class="tdc">-</td> +</tr><tr> +<td class="tdc br">4444</td> +<td class="tdl">Ti+</td> +<td class="tdr br">*</td> +<td class="tdc">..</td> +<td class="tdc">\(F_0\)</td> +<td class="tdc br">\(F_2-M_a\)</td> +<td class="tdc">0</td> +<td class="tdc">0</td> +<td class="tdc">+1</td> +<td class="tdc">s</td> +<td class="tdc">-3</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +</tr><tr> +<td class="tdc br">4455</td> +<td class="tdl">Ca</td> +<td class="tdr br">n</td> +<td class="tdc">\(F_0-M_a\)</td> +<td class="tdc">..</td> +<td class="tdc br">..</td> +<td class="tdc">-2</td> +<td class="tdc">..</td> +<td class="tdc">-1</td> +<td class="tdc">w</td> +<td class="tdc">-1</td> +<td class="tdc">-3</td> +<td class="tdc">-</td> +</tr><tr> +<td class="tdc br">4476</td> +<td class="tdl">Fe</td> +<td class="tdr br">n</td> +<td class="tdc">\(F_0-M_a\)</td> +<td class="tdc">..</td> +<td class="tdc br">..</td> +<td class="tdc">-1</td> +<td class="tdc">..</td> +<td class="tdc">+1</td> +<td class="tdc">-1</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +</tr><tr> +<td class="tdc br">4481</td> +<td class="tdl">Mg+</td> +<td class="tdr br">*</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc br">\(F_0-M_a\)</td> +<td class="tdc">-1</td> +<td class="tdc">0</td> +<td class="tdc">0</td> +<td class="tdc">0</td> +<td class="tdc">+0</td> +<td class="tdc">+1</td> +<td class="tdc">..</td> +</tr><tr> +<td class="tdc bb br">4490</td> +<td class="tdl bb">Fe</td> +<td class="tdr bb br">n</td> +<td class="tdc bb">\(F_0-M_a\)</td> +<td class="tdc bb">..</td> +<td class="tdc bb br">..</td> +<td class="tdc bb">0</td> +<td class="tdc bb">..</td> +<td class="tdc bb">..</td> +<td class="tdc bb">+1</td> +<td class="tdc bb">-0</td> +<td class="tdc bb">+2</td> +<td class="tdc bb">..</td> +</tr> + </tbody> +</table> + +<p>It is seen from the table that the general agreement with the +anticipations of theory is satisfactory, and that the deviations, when +they occur, rarely exceed one unit. The agreement is not less good +than would be expected of the material, since the measures are here +used differentially. The majority of the discrepancies are apparently +accidental; for example, the deviations shown by the first six +entries in the first column are almost certainly the result of better +definition in the giant spectrum. There remains, however, the same +<span class="pagenum" id="Page_151">[Pg 151]</span> +discrepancy for the lines of Sr+ that was noted in the earlier part of +the chapter. There can be no doubt that these lines are stronger in +giants than in dwarfs.</p> + +<p>The strengthening of the ionized lines of the alkaline earths is +explained, when the spectra are examined, by the fact that the neutral +lines are still fairly strong long after the ionized lines have passed +their maximum—neutral strontium<a id="FNanchor_426" href="#Footnote_426" class="fnanchor">[426]</a> is found at \(F_0\) and neutral +calcium<a id="FNanchor_427" href="#Footnote_427" class="fnanchor">[427]</a> at \(A_0\). The lowered pressure, then, must increase +the concentration of singly ionized atoms at the expense of the +residual neutral atoms. There is, however, apparently no satisfactory +theoretical explanation of the survival of large quantities of neutral +calcium long after the ionized atoms have passed their maximum. The +effects predicted above would appear to be the only ones that can be +anticipated if the theory holds rigidly. Clearly some factor such as +effective level must be further considered.</p> + + +<p class="nindc space-above2"> +THE STRONTIUM LINES</p> + + +<p>The strontium problem is perhaps one that will lead to more +comprehensible results when it is treated as a whole. It is impossible +to resist the feeling that there is some definite abnormality +associated with strontium. The “strontium stars” in the still earlier +classes, where the lines 4215, 4077 appear with great intensity, +and the \(F_0\) stars \(\alpha\) Circini and \(\gamma\) Equulei, as +well as the apparently erroneous absolute magnitudes obtained by +the spectroscopic method for several other stars of low intrinsic +luminosity, all point in some such direction.</p> + +<p>It may be that these phenomena are a result of an abnormal abundance or +distribution of the element. It is not, therefore, entirely necessary +to assume that the theory is here at fault, although until the behavior +of strontium has been satisfactorily interpreted, that possibility +cannot be rejected. It is significant that calcium and barium show +similar absolute magnitude behavior. In any case, the ionized strontium +lines cannot be cited, as has sometimes been done, in demonstrating +<span class="pagenum" id="Page_152">[Pg 152]</span> +that the absolute magnitude effect is due to pressure. What is actually +shown is that the concentration of singly ionized atoms is more greatly +increased at the expense of the neutral atoms than it is reduced by the +formation of doubly ionized atoms. Since a pressure effect operates +by the discouragement of recombination, it would be inferred that the +recombination of singly ionized atoms with electrons to form neutral +atoms is less readily encouraged than the recombination of doubly +ionized atoms with electrons to form singly ionized atoms. Evidently +the problem is a complex one. If the maximum of the strontium lines +were at \(F_5\) (where theory first predicted it, and where the earlier +measures actually placed it) there would be no anomaly to explain; +but two independent observers<a id="FNanchor_428" href="#Footnote_428" class="fnanchor">[428]</a> place it definitely at \(K_2\) +or \(K_0\), and there can be little doubt that this is actually the +correct position of the maximum.</p> + +<p class="space-above2"> +The result of the study of absolute magnitude effects is disappointing. +It appears that the observed phenomena are qualitatively explained in a +satisfactory manner, as due to lowered pressure, or, more accurately, +to low surface gravity. There is, however, a serious discrepancy in the +case of the lines whose variation with absolute magnitude is perhaps +best established, and upon which the most important results have been +based. The results, being empirical, are of course unimpaired, and +it would seem that the theory requires to be amended. Furthermore, +it does not yet appear to be possible to use the observed changes of +intensity for the direct estimation of pressure differences, because +of the large number of variables involved and particularly because +of the superposition of the pure pressure effect upon the effect of +photospheric depth.</p> + + +<div class="footnotes"><h3>FOOTNOTES:</h3> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_412" href="#FNanchor_412" class="label">[412]</a> +Adams and Kohlschütter, Mt. W. Contr. 89, 1914.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_413" href="#FNanchor_413" class="label">[413]</a> +B. A. N. 19, 1922.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_414" href="#FNanchor_414" class="label">[414]</a> +Milne, Phil. Mag., 47, 209, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_415" href="#FNanchor_415" class="label">[415]</a> +Pannekoek, B. A. N. 19, 1922.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_416" href="#FNanchor_416" class="label">[416]</a> +Pop. Ast., 31, 88, 1923.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_417" href="#FNanchor_417" class="label">[417]</a> +Pop. Ast., in press.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_418" href="#FNanchor_418" class="label">[418]</a> +B. A. N. 19, 1922.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_419" href="#FNanchor_419" class="label">[419]</a> +In Pannekoek’s notation, a is surface brightness, \(R\) +is radius, and \(g\), surface gravity.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_420" href="#FNanchor_420" class="label">[420]</a> +Stewart, Pop. Ast., in press.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_421" href="#FNanchor_421" class="label">[421]</a> +Pub. Dom. Ap. Obs., 3, 1, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_422" href="#FNanchor_422" class="label">[422]</a> +<a href="#Page_121">P. 121</a>.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_423" href="#FNanchor_423" class="label">[423]</a> +H. C. 258, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_424" href="#FNanchor_424" class="label">[424]</a> +Adams, Pub. A. S. P., 28, 278, 1916; Adams and Joy, Pub. +A. S. P., 36, 142, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_425" href="#FNanchor_425" class="label">[425]</a> +Pub. Solar Phys. Com., 1910.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_426" href="#FNanchor_426" class="label">[426]</a> +Chapter V, <a href="#Page_81">p. 81</a>.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_427" href="#FNanchor_427" class="label">[427]</a> +Chapter, V, <a href="#Page_70">p. 70</a>.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_428" href="#FNanchor_428" class="label">[428]</a> +Menzel, H. C. 258, 1924; Chapter VIII, <a href="#Page_126">p. 126</a>.</p> + +</div> +</div> + +<hr class="chap x-ebookmaker-drop"> + +<div class="chapter"> +<p><span class="pagenum" id="Page_153">[Pg 153]</span></p> + +<h2 class="nobreak" id="PART_III">PART III<br> +ADDITIONAL DEDUCTIONS FROM +IONIZATION THEORY</h2> +</div> + +<hr class="chap x-ebookmaker-drop"> + +<div class="chapter"> +<p><span class="pagenum" id="Page_155">[Pg 155]</span></p> + +<h2 class="nobreak" id="CHAPTER_XI">CHAPTER XI<br> +THE ASTROPHYSICAL EVALUATION OF PHYSICAL CONSTANTS</h2> +</div> + +<p class="nind"> +IN the opening chapter the statement was made that “the astrophysicist +is obliged to assume [the validity of physical laws] in applying them +to stellar conditions.” The astrophysical evaluation of physical +constants might therefore seem, from our avowed premises, to involve +a circular argument. In certain special cases, however, the process +appears to be legitimate, and the results of three investigations are +contained in the present chapter. The first of these investigations +involves the derivation of spectroscopic constants, assuming the series +formula; the second consists of an extrapolation of the results of +<a href="#CHAPTER_X">Chapter X</a> to the estimation of unknown ionization potentials; and the +third constitutes a discussion made possible by the knowledge of the +stellar atmosphere that has been attained with the aid of ionization +theory.</p> + + +<p class="nindc space-above2"> +THE RYDBERG CONSTANT FOR HELIUM</p> + + +<p>The wave-lengths of a series of lines can be measured in the spectrum +of a star, and the series identified with a series observed in the +laboratory. The occurrence in stellar spectra of series that can be +identified with the series given by terrestrial atoms presumably +shows that similar relations govern the atomic processes in the two +sources. That series formulae of the same type are applicable to the +stellar and terrestrial atom is indeed rather an observational fact +than an assumption. By inserting into the appropriate series formula +the observed stellar frequencies, a physical constant involved may be +evaluated, and the extent of the agreement with the corresponding value +from the laboratory may be determined.</p> + +<p><span class="pagenum" id="Page_156">[Pg 156]</span></p> + +<p>H. H. Plaskett<a id="FNanchor_429" href="#Footnote_429" class="fnanchor">[429]</a> has measured the wave-lengths of the lines of the +Pickering series (\(_4F-mG\)) of He+ in the spectra of three \(O\) +stars, incidentally separating the alternate Pickering lines from +the Balmer lines for the first time. The formula that connects the +frequencies of the lines with the constants associated with the atom is +\[ +\nu = N (E/e)^{2}\left(\frac{1}{n^{2}} - \frac{1}{m^{2}}\right) +\] +\[ +\begin{array}{l} +\nu &= \text{frequency}\\ +N &= \text{the Rydberg Constant}\\ +E &= \text{mass of atom}\\ +e &= \text{mass of electron}\\ +n &= 3\\ +m &= 4, 5, 6. \ldots +\end{array} +\]</p> + +<p>Plaskett discussed the theory, and derived from the measured +wave-lengths of five lines the mean value of 109722.3 ± 0.44 for the +constant \(N\). The value determined in the laboratory by Paschen +is 109722.14 ± 0.04. Plaskett’s comment on the agreement is as +follows: “It was not to be expected that there would be any startling +changes.... It is of interest, however, to note that these “stellar” +determinations <i>are</i> in agreement with the terrestrial values, in +so far as it shows that <i>the implicit assumption of identical atomic +structure, identical electrons, and identical laws of radiation on the +earth and in the stars, is in some measure justified</i>.”</p> + + +<p class="nindc space-above2"> +CRITICAL POTENTIALS</p> + + +<p>The theory outlined in the preceding chapters was used in determining +the astrophysical behavior of lines corresponding to known series +relations. When the validity of the theory has been established, it +is possible, as was pointed out by the writer,<a id="FNanchor_430" href="#Footnote_430" class="fnanchor">[430]</a> by Fowler and +Milne,<a id="FNanchor_431" href="#Footnote_431" class="fnanchor">[431]</a> and by Menzel,<a id="FNanchor_432" href="#Footnote_432" class="fnanchor">[432]</a> to deduce the ionization potentials of +lines of unknown series relations from their astrophysical behavior. +The ionization potentials were estimated in this way for the table in +<a href="#CHAPTER_I">Chapter I</a>.</p> + +<p>In general the observations show that the higher the ionization +<span class="pagenum" id="Page_157">[Pg 157]</span> +potential, the higher the temperature at which the corresponding lines +attain maximum. This is in strict accordance with theory. It is not +possible to predict the exact form of the relation between temperature +of maximum and ionization potential. For the observed cases in which +\(T_{max} = 0\) (the ultimate lines), \(\chi_{1}-\chi_{1}^{(r)}\). It +would appear that \(T_{max}\) should approach zero as \(\chi_{1}\) +approaches zero. But in this case \(\chi_{1}^{(r)}\) (the +negative energy of the excited state, which must always be less +than \(\chi_{1}\)) also approaches zero, and the relation becomes +indeterminate. The form of the curve as \(\chi_{1}\) approaches zero has merely a +theoretical interest, as no known element has an ionization potential +of less than four volts. In the present application the relation will +be treated as an empirical one. The curves given by the writer and by +Menzel for the relation between ionization potential and \(T_{max}\) +display a good general regularity, and the deviations, as was pointed +out in a previous chapter,<a id="FNanchor_433" href="#Footnote_433" class="fnanchor">[433]</a> probably arise from differences of +effective level. Owing to this source of irregularity, great accuracy +is not to be anticipated in the deduced ionization potentials. +The effective level is at the greatest height for lines of low +excitation potential. The excitation potentials corresponding to the +astrophysically important lines of the once, twice, and thrice ionized +atoms in the hotter stars are in all known cases highland thus the +error introduced by neglecting to correct for effective level is small. +The error introduced by an excitation potential of the wrong order +is, moreover, a constant and not a percentage error, and thus becomes +less serious in estimating high ionization potentials. Accordingly the +deduced ionization potentials will probably be of the right order.</p> + +<p>The relation connecting ionization potential and \(T_{max}\) may, for +our purposes, be treated as an empirical relation between ionization +potential and spectral class. This mode of regarding the question has +the advantage of being quite independent of the adopted temperature +scale. We merely assume that the sequence of spectral classes is a +temperature sequence. The ionization potentials corresponding to lines +<span class="pagenum" id="Page_158">[Pg 158]</span> +of known maximum may then be deduced by interpolation.</p> + +<h2><a id="TABLE_XXV">TABLE XXV</a></h2> + +<table class="autotable"> +<thead><tr> +<th class="tdc">Element </th> +<th class="tdc"> Ionization Potential </th> +<th class="tdc">Authority</th> +</tr> +</thead> +<tbody><tr> +<td class="tdl">C++</td> +<td class="tdc">45</td> +<td class="tdl">Payne</td> +</tr><tr> +<td class="tdl">N+</td> +<td class="tdc">24</td> +<td class="tdl">Ibid.</td> +</tr><tr> +<td class="tdl">N++</td> +<td class="tdc">45?</td> +<td class="tdl">Ibid.</td> +</tr><tr> +<td class="tdl">O+</td> +<td class="tdc">32</td> +<td class="tdl">Ibid.</td> +</tr><tr> +<td class="tdl">O++</td> +<td class="tdc">45</td> +<td class="tdl">Fowler and Milne</td> +</tr><tr> +<td class="tdl">Si</td> +<td class="tdc">8.5</td> +<td class="tdl">Menzel, Payne</td> +</tr><tr> +<td class="tdl">S+</td> +<td class="tdc">20</td> +<td class="tdl">Payne</td> +</tr><tr> +<td class="tdl">S++</td> +<td class="tdc">32</td> +<td class="tdl">Ibid.</td> +</tr><tr> +<td class="tdl">Sc+</td> +<td class="tdc">12.5</td> +<td class="tdl">Menzel</td> +</tr><tr> +<td class="tdl">Ti+</td> +<td class="tdc">12.5</td> +<td class="tdl">Ibid.</td> +</tr><tr> +<td class="tdl">Fe</td> +<td class="tdc">7.5</td> +<td class="tdl">Ibid.</td> +</tr><tr> +<td class="tdl">Fe+</td> +<td class="tdc">13</td> +<td class="tdl">Ibid.</td> +</tr> + </tbody> +</table> + +<p>The value of \(T_{max}\) is dependent on the effective level, and hence +upon the excitation potential. Without the introduction of unjustified +assumptions, more than one critical potential cannot be deduced +from observations of intensity maximum. The excitation potential +corresponding to a line could be roughly inferred from the observed +maximum, by observing the shift of predicted maximum produced by the +level effect (discussed in <a href="#CHAPTER_IX">Chapter IX</a>) if the ionization potential were +known. There are, however, no data as yet that could be used in drawing +inferences of this kind.</p> + + +<p class="nindc space-above2"> +DURATION OF ATOMIC STATES</p> + + +<p>The successful application of theory to the astrophysical determination +of the life of an atom requires the fulfilment of special conditions. +The requirements of the idea developed by Milne<a id="FNanchor_434" href="#Footnote_434" class="fnanchor">[434]</a> demand that +the atom shall exist in appreciable quantities in only two states +simultaneously. This condition is fulfilled by the ionized atoms of the +alkaline earth elements, and it is with calcium that the estimates here +discussed are concerned.</p> + +<p><span class="pagenum" id="Page_159">[Pg 159]</span></p> + +<p>The investigation relates to the calcium present in the high-level +chromosphere, where, owing to remoteness from the photosphere, thermal +ionization is negligible. Photoelectric ionization may be operative in +removing the first electron from the calcium atom, but the sun is too +deficient in light of wave-length 1040 for second stage photoelectric +ionization to be appreciable. The calcium present in the high-level +chromosphere is probably largely in the once ionized condition, since +an atom once ionized is likely to remain so for a long time, owing to +the scarcity of free electrons in the tenuous outer regions of the sun. +The present investigation neglects altogether the neutral and doubly +ionized calcium atoms, and furthermore assumes that the transfers +corresponding to the \(H\) and \(K\) lines of the \(1^{2}S-1^{2}P\) +series are the only ones that occur in appreciable quantities. The +latter assumption is apparently not accurately fulfilled, as the +\(1^{2}P-m^{2}D\) lines of Ca+ have recently been detected in the high +level chromosphere.<a id="FNanchor_435" href="#Footnote_435" class="fnanchor">[435]</a></p> + +<p><span class="pagenum" id="Page_160">[Pg 160]</span></p> + +<p>In the simple case of the Ca+ atom (neglecting the small number of +atoms that are giving rise to the \(1^{2}P-m^{2}D\) lines) only two states +of the atom are possible: the normal state, called by Milne the \(1 +\sigma\) state, and the excited, or \(1 \pi\) state. A given atom +exists alternately in these two states. If \(\tau\) be the average time +spent in the \(1 \pi\) state, and \(\tau'\) the average time spent in +the \(1 \sigma\) state, the average time spent by an atom in traversing +its possible cycle of changes is \(\tau + \tau'\). Now \(\tau\) is +connected with the probability of an emission, and \(\tau'\) with the +probability of an absorption. Clearly \(\tau'\) depends at least partly +upon the energy supply, but \(\tau\) is an atomic constant measuring +the readiness with which the atom recovers its normal state after an +absorption. It is, in fact, the “average life” evaluated from Milne’s +equations. The ratio \(\dfrac{\tau}{\tau'}\), expressing the relative +tendencies of Ca+ atoms to emit and to absorb the \(H\) and \(K\) +lines, is the residual intensity at their centers, with respect to the +adjacent continuous background.</p> + +<p>Einstein’s theory of radiation<a id="FNanchor_436" href="#Footnote_436" class="fnanchor">[436]</a> is used in evaluating +\(\dfrac{\tau}{\tau'}\) from the relation +\[ +\frac{\tau}{\tau'}=\frac{\frac{1}{2} r}{e^{h \nu / k T}-1} +\] +where \(r\) is the ratio +\(\displaystyle{\dfrac{\text{line intensity}}{\text{background intensity}}}\).</p> + +<p>From ordinary quantum principles, +\[ +\left(\tau + \tau'\right) = \frac{\frac{1}{2} h \nu}{c m g} +\] +and both \(\tau\) and \(\tau'\) may be derived by eliminating between +the two equations.</p> + +<p>The only measured quantity in the formula is \(r\), and from the fact +that \(r\) is the “residual intensity” within an absorption line, +we know that it must lie between 0 and 1. Hence a maximum value of +\(\displaystyle{5.4~\times~10^{-8}~ \text{seconds}}\) may be derived +for \(\tau\). On the insertion of the data given by Schwarzschild<a id="FNanchor_437" href="#Footnote_437" class="fnanchor">[437]</a> +for the residual intensity of the \(H\) and \(K\) lines, 2.6 +magnitudes fainter than the continuous background, and corresponding +to a value of \(r\) equal to 0.11, the deduced value of \(r\) is +\(\displaystyle{0.6~\times~10^{-8}~ \text{seconds}}\). The agreement +of this value with those obtained in the laboratory for the atoms of +hydrogen and mercury has been commented upon in a previous chapter.<a id="FNanchor_438" href="#Footnote_438" class="fnanchor">[438]</a></p> + + +<div class="footnotes"><h3>FOOTNOTES:</h3> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_429" href="#FNanchor_429" class="label">[429]</a> +H. H. Plaskett, Pub. Dom. Ap. Obs., 2, 325, 1922.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_430" href="#FNanchor_430" class="label">[430]</a> +M. N. R. A. S., 84, 499, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_431" href="#FNanchor_431" class="label">[431]</a> +H. C. 256, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_432" href="#FNanchor_432" class="label">[432]</a> +H. C. 258, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_433" href="#FNanchor_433" class="label">[433]</a> +Chapter IX, <a href="#Page_133">p. 133</a>.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_434" href="#FNanchor_434" class="label">[434]</a> +Milne, M. N. R. A. S., 84, 354, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_435" href="#FNanchor_435" class="label">[435]</a> +Curtis and Burns, unpub.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_436" href="#FNanchor_436" class="label">[436]</a> +Phys. Zeit., 18, 121, 1914.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_437" href="#FNanchor_437" class="label">[437]</a> +Sitz. d. Preuss. Ac., 47, 1198, 1914.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_438" href="#FNanchor_438" class="label">[438]</a> +Chapter I, <a href="#Page_21">p. 21</a>.</p> + +</div> +</div> + + +<hr class="chap x-ebookmaker-drop"> + +<div class="chapter"> +<p><span class="pagenum" id="Page_161">[Pg 161]</span></p> + +<h2 class="nobreak" id="CHAPTER_XII">CHAPTER XII<br> +SPECIAL PROBLEMS IN STELLAR ATMOSPHERES</h2> +</div> + +<p class="nind"> +THE greater part of the present work has dealt with the discussion and +interpretation of the normal spectral sequence, \(B_0\) to \(M_b\), and +the main features of the series have been satisfactorily attributed +to thermal ionization at high temperatures. Such a discussion must +naturally be the first step in the analysis of the stellar atmosphere. +When the more general results of observation have been reduced, in +some measure, to an orderly system, it becomes possible to consider +special problems involving stars or groups of stars, which lie outside +the system, or which, though included in the system, display definite +abnormalities.</p> + +<p>The special problems of stellar spectroscopy are very numerous. We may +mention the novae, the Class \(O\) stars, \(B\) stars that show emission +lines, the problem of \(A\)-star classification and the peculiar +\(A\) stars, \(F\) stars that display both giant and dwarf spectral +characteristics, the classification of the \(K\) stars, the apparent +splitting into three groups of the spectral sequence for temperatures +below 4000°, the problem of the c-stars, the Cepheid variables with +their variable spectra, and the variables of long period.</p> + +<p>It is not possible, in a work like the present, to touch upon many of +these subjects, and the writer has selected for brief discussion three +upon which she can contribute new material: the problem of the \(O\) +stars, the classification of the \(A\) stars, and the interpretation of +the spectra of the stars that display the c-characteristic.</p> + + +<p class="nindc space-above2"> +THE STARS OF CLASS \(O\)</p> + + +<p>The statistically negligible class containing the \(O\) stars is +placed, at the present stage of investigation, at the top of the +stellar sequence. These spectra indicate higher excitation than +<span class="pagenum" id="Page_162">[Pg 162]</span> +those of any other class, and ionization theory distributes their +temperatures between 25,000° and 40,000°. Their spectra are among the +most puzzling encountered in the whole stellar sequence, and theory has +hitherto been unsuccessful in suggesting the conditions that produce +them.</p> + +<p>A hundred and forty non-Magellanic \(O\) stars<a id="FNanchor_439" href="#Footnote_439" class="fnanchor">[439]</a> are enumerated in +the Draper catalogue, and in addition a small number of apparently +faint \(B\) stars should probably be transferred to Class \(O\), as +Victoria has already done<a id="FNanchor_440" href="#Footnote_440" class="fnanchor">[440]</a> for a group of stars in Monoceros. The +\(O\) stars have a very definite distribution; they lie either very +near the galactic plane, or in one of the Magellanic clouds, or they +constitute the nuclei of planetary nebulae.</p> + +<p>The \(O\) stars other than the nuclei of planetaries have high +intrinsic luminosities, but the material is insufficient for a +satisfactory estimate of the absolute magnitudes of the non-Magellanic +\(O\) stars; various indications point to a value at least as high as +-4. For the Magellanic \(O\) stars, absolute magnitudes as great as +-6.7 have been derived.<a id="FNanchor_441" href="#Footnote_441" class="fnanchor">[441]</a> The measured parallaxes of the planetary +nebulae, however, give for the nuclei absolute magnitudes<a id="FNanchor_442" href="#Footnote_442" class="fnanchor">[442]</a> in the +neighborhood of +8. The wide difference in absolute magnitude can +merely be pointed out; it has never received adequate explanation.</p> + +<p>The masses are presumably very high for the \(O\) stars, though but few +have been accurately measured. The star B.D. 6°1309, a spectroscopic +binary reported by J. S. Plaskett,<a id="FNanchor_443" href="#Footnote_443" class="fnanchor">[443]</a> has a minimum mass eighty times +that of the sun, and the stars 29 Canis Majoris and \(\iota\) Orionis +also appear to be very massive.<a id="FNanchor_444" href="#Footnote_444" class="fnanchor">[444]</a></p> + +<p>The spectra of the stars of Class \(O\) differ widely among themselves, +but they are signalized by the lines of ionized helium, which are +normally observed only in this class and in the nebulae. In addition, +the atoms of H, He, Mg+, C++, 0++, N++, and Si+++ are represented. +<span class="pagenum" id="Page_163">[Pg 163]</span> +The atmospheres of these stars are thus in a state of high ionization, +which is attributed to high temperature, in harmony with the work +already outlined in previous chapters. The spectra of the stars +of Class \(O\) have been described by W. W. Campbell,<a id="FNanchor_445" href="#Footnote_445" class="fnanchor">[445]</a> Miss +Cannon,<a id="FNanchor_446" href="#Footnote_446" class="fnanchor">[446]</a> Wright,<a id="FNanchor_447" href="#Footnote_447" class="fnanchor">[447]</a> + H. H. Plaskett,<a id="FNanchor_448" href="#Footnote_448" class="fnanchor">[448]</a> J. S. Plaskett,<a id="FNanchor_449" href="#Footnote_449" class="fnanchor">[449]</a> and +the writer,<a id="FNanchor_450" href="#Footnote_450" class="fnanchor">[450]</a> and the material upon which the present discussion is +based will be found in the papers quoted.</p> + +<p>Many of the \(O\) stars, such as \(\tau\) Canis Majoris, H.D. 150135, +H.D. 159176, H.D. 199579, H.D. 164794, H.D. 167771, H.D. 165052, give a +pure absorption spectrum, containing the Balmer series of hydrogen, the +lines of Si+++, the Pickering and “4686” lines of He+, and the N++ line +at 4097. The stars are mentioned in order of increasing ionization, +with He+ rising in intensity. The other lines mentioned are clearly +beyond their maximum, and fall progressively in strength. The stars +mentioned probably represent successive steps in a sequence with rising +temperature, connecting directly with Class \(B_0\), and ranging from +25,000° to 35,000°.</p> + +<p>This sequence of \(O\) stars would form a simple and explicable series +if it were an isolated group. There are, however, other stars, with +spectra so similar to those of the series just quoted that there can +be no doubt of a close relationship—they display absorption lines due +to the same elements with about the same relative intensities—but +emission lines tend to occur in various parts of the spectrum. 29 Canis +Majoris, \(\delta\) Muscae, and \(\xi\) Puppis have absorption spectra +which resemble those in the sequence just quoted, but at 4650 and 4686 +there are emission lines or “bands.” The bright lines are so wide and +diffuse, in \(\delta\) Muscae, as to be blended together at their +edges, while they are sharp and clear in the other two stars. Between +the two series just quoted—pure absorption stars and absorption stars +<span class="pagenum" id="Page_164">[Pg 164]</span> +with some bright lines, comes \(\delta\) Circini, a star which has all +the characteristics of the first group, and also shows faint emission +on the red edge of the absorption lines at 4650 and 4686.</p> + +<p>There are other stars, such as \(\lambda\) Cephei, \(\xi\) Persei, S +Monocerotis, H.D. 152408, H.D. 112244, and \(\iota\) Orionis, that have +absorption spectra such as were described for the first group, but +which display faint emission lines at the red edge of the hydrogen and +helium lines. It is obvious that all the stars so far enumerated may +legitimately be classed together, but that there is a very universal +tendency for emission lines and bands to appear in them. This tendency +is so marked in the stars that are still to be mentioned as to +constitute their most salient feature.</p> + +<p>In the subgroup of the \(O\) stars which are collectively designated +the Wolf-Rayet stars, the emission lines are the most conspicuous +characteristic of the spectrum. The best known and brightest star +of this group is \(\gamma\) Velorum, which possesses an extremely +complex spectrum, made up of an absorption spectrum similar to that +of \(\delta\) Circini, and a large number of wide “emission bands.” An +analysis of the spectrum of \(\gamma\) Velorum has been published by +the writer;<a id="FNanchor_451" href="#Footnote_451" class="fnanchor">[451]</a> all the stronger lines of H, He, He+, C+H-, O++, N++, +Si+++, and Mg+ are represented in the spectrum, and a comparatively +small number of lines remains unidentified.</p> + +<p>Other \(O\) stars that have spectra in which the emission lines are +the prominent feature are H.D. 151932, H.D. 92740, H.D. 93131, H.D. +152270, H.D. 156385, and H.D. 97152. All of these stars, excepting the +last, have also absorption spectra displaying the lines of H and He+. +The lines of N++ and Si+++ are absent, and these stars are therefore +probably at the extreme high-temperature end of the sequence.</p> + +<p>The question of absorption in the Wolf-Rayet spectrum is a difficult +one, because the bright lines show up before any other feature of the +spectrum, while an appreciable continuous background is necessary +before absorption can be detected. The detection of absorption lines +<span class="pagenum" id="Page_165">[Pg 165]</span> +in many stars, such as H.D. 152270, where no absorption had previously +been recorded, has resulted from a general survey of spectra that had +received exposures sufficient to bring out the continuous background. +The writer has been led to the opinion that absorption is a common, +if not universal, feature of all the Wolf-Rayet stars, except those +classed at Harvard as \(Ob\). This subclass has bright bands that +do not coincide with those of the other \(O\) stars, and among them +absorption lines appear to be exceptional.</p> + +<p>It is perhaps to be expected that absorption should normally occur +among the Wolf-Rayet stars, as it does among the other classes. In all +other stars, the bright lines that appear are the abnormal feature, and +are superposed on a normal continuous spectrum crossed by absorption +lines. Spectra consisting of bright lines <i>only</i> do not occur +elsewhere, excepting for the gaseous nebulae. The gaseous nebulae have, +presumably, no photosphere, and the continuous background that they +sometimes display is probably the result of reflected and transformed +starlight; absorption lines appear normally to accompany the existence +of a photosphere.</p> + +<p>It is clear that the \(O\) stars are a very complex group. Those that +have pure absorption spectra can be arranged in a series immediately +preceding \(B_0\); and those that show a similar absorption spectrum, +with faint superposed emission, presumably also fit into the sequence. +When a \(B\) star shows emission lines (as \(\gamma\) Cassiopeiae does) +it is placed in the \(B\) class appropriate to its absorption spectrum, +with the additional designation “e” to indicate the abnormality, and +the same procedure appears to be equally satisfactory for the \(O\) +stars.</p> + +<p>As emission predominates more and more, the spectrum resembles those +of the normal members of the sequence less and less. If a star has an +absorption spectrum it can always be assigned a place in the sequence, +and this method of arrangement appears to be logical. But it is clear +that the sequence so formed is no longer physically homogeneous. +The stars that have no absorption lines, although some of them have +obvious affinities with stars that have absorption spectra, have +<span class="pagenum" id="Page_166">[Pg 166]</span> +moreover no place in a sequence formed on the basis of absorption +intensities.</p> + +<p>It is, of course, possible to devise a self-consistent scheme for the +arrangement of a limited number of the \(O\) stars, and such a scheme +is, for many purposes, both desirable and convenient. It is, however, +exceedingly hard to know where the division should be drawn between +“absorption” and “emission” stars. Perhaps the most satisfactory plan +is to treat all \(O\) stars as a <i>sequence</i>, with special comment +for the large number of them that require it.</p> + + +<p class="nindc space-above2"> +THE CLASS \(A\) STARS</p> + + +<p>(a) <i>The Balmer Lines.</i>—The spectra of the \(A\) stars are +dominated by the Balmer series of hydrogen, which, with the exception +of the \(H\) and \(K\) lines in the cooler stars, are stronger at +\(A_0\) than any other line seen in the stellar sequence. The maximum +of the Balmer series has been stated<a id="FNanchor_452" href="#Footnote_452" class="fnanchor">[452]</a> to occur at \(A_0\), and +this value was used by Fowler and Milne<a id="FNanchor_453" href="#Footnote_453" class="fnanchor">[453]</a> in calibrating their +temperature scale based upon ionization theory. It is in accordance +with theory that the subordinate lines of hydrogen, with ionization +potential 13.54 volts, and excitation potential 10.15 volts, should +have their maximum at about 10,000°.</p> + +<p>The position of the maximum can be placed elsewhere by the use of +special stars in estimating the line-intensities. The intensity of the +hydrogen lines is in fact unusually difficult to determine, as they +differ from star to star in width, wings, and probably also in central +intensity. Using a series of individual stars, Menzel<a id="FNanchor_454" href="#Footnote_454" class="fnanchor">[454]</a> placed the +maximum at \(A_3\), with the note that “on the average the lines seem +to be strongest in Classes \(A_2\) to \(A_4\), but the mean intensity +is often greatly exceeded in certain \(A_5\), \(A_0\) and even +\(B_8\) stars.” A general study of the Class \(A\) spectra confirms +the statement that the mean intensity at maximum is often exceeded +for individual stars in other classes, and the writer is inclined to +be of the opinion that no significant maximum can be derived from a +<span class="pagenum" id="Page_167">[Pg 167]</span> +limited number of estimates. The maximum given in the Henry Draper +Catalogue is the product of the examination of an enormous number of +very short dispersion plates, and is entitled to a greater weight +than any other. In the estimation of such strong lines, the width and +especially the wings are likely to affect the estimates extensively, +and short dispersion plates probably reduce the difficulty, and permit +of the greatest possible accuracy. It must be emphasized that the +maximum given in the Henry Draper Catalogue cannot be superseded by +measures made on an arbitrary selection of stars, such as is used +when stars bright enough to be photographed with (say) two objective +prisms are discussed, for it is a generalization from the most complete +data hitherto examined, or to be examined for some time to come. The +non-homogeneity of the \(A\) classes, presently to be discussed, +includes wide variations in the widths of the hydrogen lines, and +renders unnecessary any attempt to correct the hydrogen maximum at +\(A_0\), which appears to be of a statistical nature.</p> + +<p>(b) <i>Metallic Lines and Band Absorption.</i>—The metallic lines, +which become so conspicuous in intensity in the later classes, appear +in the types immediately succeeding \(A_0\), and increase progressively +in strength as cooler classes are approached. In general, all the +related lines belonging to any one element appear at the same class, +although sometimes the fainter components of metallic multiplets are +not seen until the stronger components have attained a considerable +intensity. For example the weaker lines of an element that is seen at +\(A_0\) may not appear till \(A_2\). The disparity in intensity between +the components of a multiplet is usually not so great at appearance +as at maximum. The relative strengths of unblended lines conform at +maximum with the laboratory intensities, to an extent that raises +questions as to the degree of saturation<a id="FNanchor_455" href="#Footnote_455" class="fnanchor">[455]</a> of the more intense +components. It seems that none of the metallic lines, excepting those +of calcium, are greatly oversaturated, even at maximum, to judge from +the relative intensities of related lines at that point.</p> + +<p><span class="pagenum" id="Page_168">[Pg 168]</span></p> + +<p>It is within the \(A\) stars that the first signs of band absorption +appear. The \(G\) band is seen in some \(A\) stars, and a drop in the +continuous spectrum of Vega around 4160 has been ascribed<a id="FNanchor_456" href="#Footnote_456" class="fnanchor">[456]</a> to the +cyanogen band headed at 4215. Similar “band” absorption can be traced +in other stars of Class \(A\), and is even seen as early as \(B_0\). +Identification of the cyanogen band headed at 3885, which always +accompanies the 4125 band, would confirm the attribution to cyanogen, +but the violet band does not seem to have been observed. The wings of H +\(\xi\), which are often wide and conspicuous, render it difficult to +trace anything of the nature of band absorption near 3885 for an \(A\) +star.</p> + +<p>(c) <i>The Classification of \(A\) Stars.</i>—Several lines of +evidence have indicated that the classes into which the \(A\) stars +have been divided are not physically homogeneous, and the problem of +their classification is one of the future tasks of astrophysics. It is +hoped that the writer can in the future make a more complete discussion +of the question than is here desirable, and therefore the present +treatment is to be considered merely suggestive and tentative. The +material quoted is slight, and must be increased before conclusions can +be justified.</p> + +<p>It has been suggested<a id="FNanchor_457" href="#Footnote_457" class="fnanchor">[457]</a> that a one-dimensional arrangement will +not suffice for the classification of the \(A\) stars. The spectra +have been classified, at least for the hotter \(A\) types, by the +strength of the \(H\) and \(K\) lines of Ca+. With the dispersion +used in making the Henry Draper Catalogue, these lines constitute +the conspicuous difference between one spectrum and another, and +are the obvious criterion of class. If the spectra are classed by +the strength of these lines alone, the classification is of course +quite unambiguous, and for a one-dimensional sequence of spectra it +would have been ideal. That the classes so formed are <i>not</i> +homogeneous<a id="FNanchor_458" href="#Footnote_458" class="fnanchor">[458]</a> indicates that some second variable must be described +in a satisfactory classification, and that the strength of no one line +could have been used with any greater success than that of the \(H\) +<span class="pagenum" id="Page_169">[Pg 169]</span> +and \(K\) doublet. Further, practical difficulty in duplicating the +classifications has been caused by the fact that the \(H\) and \(K\) +lines are so far into the violet that they do not appear at all on +many slit spectra, such as those used at Mount Wilson, and when other +criteria are chosen for classification, it is likely that the results +will deviate somewhat from those of the Henry Draper Catalogue.</p> + +<p>By analogy with what is observed in other types, it has been suggested +that the range in line-sharpness that is found within a given class +among the \(A\) stars is an effect of absolute magnitude, and the +sharpness of the hydrogen lines has indeed been used at Mount +Wilson<a id="FNanchor_459" href="#Footnote_459" class="fnanchor">[459]</a> as a quantitative measure of luminosity. From an analysis +of the widths of hydrogen lines made by Miss Fairfield,<a id="FNanchor_460" href="#Footnote_460" class="fnanchor">[460]</a> it appears +that the line sharpness may be used to distinguish \(A\) stars of the +highest luminosity from those of the lowest, but that it cannot be used +for the accurate estimation of absolute magnitude between those limits.</p> + +<p>The special problem of classifying the \(A\) stars is only in its +initial stage. That the present system is inadequate is certain, but +as yet no satisfactory alternative has been proposed. The direction in +which work should be pursued is, in this instance, probably the study +of the differences between individual spectra. As the problem appears +to hinge on the presence of abnormalities within a given class, it is +of especial importance to examine the frequency, magnitude, and nature +of these abnormalities.</p> + +<p>(d) <i>Silicon and Strontium Stars.</i>—There are among the \(A\) +stars two small groups of especial interest—the so-called “silicon” +and “strontium” stars. These occur chiefly in \(A_0\), \(A_2\), +\(A_3\), and are distinguished by the unusual intensity of the +lines 4128 and 4131 of ionized silicon, and the lines 4077 and 4215 +of ionized strontium. Such stars are regarded in the Henry Draper +Catalogue as definitely abnormal, and are individually mentioned in +the Remarks. The strontium stars in classes later than \(F_0\) are +<span class="pagenum" id="Page_170">[Pg 170]</span> +apparently ordinary high-luminosity stars, and the line-intensity is +involved in the well known absolute magnitude effect.</p> + +<p>The absolute magnitudes of the strontium stars have been supposed, on +general grounds, to be very high, but an examination of the proper +motions indicates that this is perhaps not even generally true. The +well known \(F\) star \(\alpha\) Circini is apparently a dwarf,<a id="FNanchor_461" href="#Footnote_461" class="fnanchor">[461]</a> +and \(\gamma\) Equulei has similar spectral peculiarities and proper +motion. Examples might be multiplied, but there is not enough material +at present available for a full discussion, and from what has already +been said it is evident that the strontium stars constitute no ordinary +absolute magnitude problem, although the condition that produces strong +strontium lines in some dwarf stars may be something, like low surface +gravity, that also prevails in stars of high luminosity.</p> + +<p>There are too few parallaxes, proper motions and radial velocities +for significant statistical treatment of the silicon stars, and still +less material for the strontium stars; but the galactic distributions +of both classes indicate that their absolute magnitudes are at least +not extremely high. There does not at present appear to be sufficient +justification for the statement that these stars are “distinctly +brighter than the average.”<a id="FNanchor_462" href="#Footnote_462" class="fnanchor">[462]</a> Their brightness would rather seem to +be about the same as that of a normal \(A\) star.<a id="FNanchor_463" href="#Footnote_463" class="fnanchor">[463]</a></p> + +<p>The silicon and strontium stars raise spectroscopic difficulties that +differ somewhat in the two cases. Most of the silicon stars occur at or +near \(A_0\), where the Si+ lines are normally at maximum intensity. +On the other hand, Sr+ has its maximum at Class \(K_2\) or \(K_5\), +but the intensity in such \(A\) stars as \(\omega\) Ophiuchi and +\(\omega_1\) Microscopii is as great as it is in these types. The +strontium problem illustrates the general conceptions underlying the +methods of estimating line-intensities, and will therefore be discussed +in slightly more detail.</p> + +<p><span class="pagenum" id="Page_171">[Pg 171]</span></p> + +<p>Abnormal intensity of a spectrum line can be attributed to (1) +blending, (2) unusual conditions, or (3) abnormal abundance. These +conditions will be discussed in order.</p> + +<p>(1) <i>Blending.</i>—Blending, excepting where lines are +spectroscopically resolved, can only be detected indirectly, by +examining the behavior of other lines belonging to the same spectral +series as the line in question. If the relative intensities of all the +lines in the series are the same as those found in the laboratory, and +if changes of intensity from class to class affect all the lines of +a series equally, it may be inferred that blending is not a serious +disturbing factor and that the abnormal intensity is due to other +causes. The close correlation between the stellar intensities of 4215 +and 4077, the components of the principal doublet of ionized strontium, +in the different spectral classes, leaves little doubt that these lines +are effectively unblended in the \(A\) stars, although the difference of +spectral class for the maximum of the two lines (\(K_2\), \(M_a\)) and +the presence of a solar iron line at 4215, suggest a blend for the +latter in stars cooler than about \(F_5\). It is also to be remarked +that the head of a “cyanogen” band falls at 4216.</p> + +<p>(2) <i>Abnormal Conditions.</i>—Abnormal conditions permit of no +direct observational test, but it would be anticipated that they would +also affect other lines to a degree greater than is observed. The +change of temperature that would be required to raise the Sr+ lines +to their maximum strength at \(A_0\) (10,000°) would be a fall of +about 5000°, which is quite inadmissible, for the resulting change of +spectrum would produce a \(K\) star. The required change of pressure +is also too great to be possible: this subject cannot profitably +be discussed here, and reference should be made to<a href="#CHAPTER_X">Chapter X</a>. The +existence of a strontium cloud has been suggested<a id="FNanchor_464" href="#Footnote_464" class="fnanchor">[464]</a> by analogy with +the “calcium cloud,” and might possibly provide an explanation, as +it would furnish a low temperature for the strontium without unduly +lowering the temperature for the star in general. The observation of +stationary strontium lines would materially strengthen this argument, +<span class="pagenum" id="Page_172">[Pg 172]</span> +but they have not so far been recorded. The fact that the strontium +stars are scattered, and not concentrated in any one part of the sky, +reduces the probability of this suggestion.</p> + +<p>(3) <i>Abnormal Abundance.</i>—Abnormal abundance has been +progressively abandoned as an explanation of the various phenomena of +stellar spectra, and that it is the true interpretation of strontium +peculiarities seems somewhat unlikely. For the silicon stars, unusual +abundance is probably an untenable hypothesis, since the great strength +of the Si+ lines is apparently not accompanied by increase in the +silicon line, which should presumably occur if pure abundance is the +cause of the increased strength of the ionized silicon lines. Abnormal +strength of silicon in the cooler stars, doubly ionized silicon in the +early \(B\) stars, or triply ionized silicon in the \(O\) stars, has not +been observed, and it is not very probable that, if silicon is unevenly +distributed in the universe, the irregularity would be revealed in +stars at one temperature only.</p> + +<p>Such considerations point to the problem of the silicon and strontium +stars as one involving the atom and its energy supply, rather than an +abnormal distribution of the element in question. It is likely that the +problem of classifying the \(A\) stars will be elucidated by a more +detailed study of the silicon and strontium lines. The behavior of +strontium appears, however, in some cases, to warrant the description +of “abnormal,” and it may be that the first step in the \(A\) star +problem will be the elimination from the general classification of +spectra such as those of the strontium stars. The present writer +inclines to the belief that the silicon and strontium stars will be +included in the normal \(A\) star classification, when such a one is +satisfactorily devised.</p> + +<p>(e) <i>Peculiar Class \(A\) Stars.</i>—Among the \(A\) stars there are +three which appear to be of special interest.</p> + +<p>The star \(\alpha\) Andromedae, designated \(A_{op}\) in the Draper +Catalogue, has been shown to display enhanced lines of manganese, +broadly winged, and of unusual strength.<a id="FNanchor_465" href="#Footnote_465" class="fnanchor">[465]</a></p> + +<p><span class="pagenum" id="Page_173">[Pg 173]</span></p> + +<p>The star \(\alpha\) Canum Venaticorum has been the subject of extensive +work.<a id="FNanchor_466" href="#Footnote_466" class="fnanchor">[466]</a><a id="FNanchor_467" href="#Footnote_467" class="fnanchor">[467]</a> The chief point of interest concerning it is the +occurrence of lines ascribed to the rare earths.<a id="FNanchor_468" href="#Footnote_468" class="fnanchor">[468]</a> The spectra of +these elements are so rich in lines that spurious coincidences are +certain to occur, but comparisons with the spectrum of \(\alpha\) Cygni +and of the chromosphere suggest that the strongest lines of europium +and terbium are indeed represented. From general ionization principles +it would appear that enhanced spectra are probably involved, but until +series relations are known it is not possible to discuss the subject +further.</p> + +<p>The super-giant, or c-star, \(\alpha\) Cygni, Class \(A_{2p}\), has +probably greater possibilities for the stellar spectroscopist than any +other star, as its spectrum is peculiarly rich in fine sharp lines, +many of which are unidentified, \(\alpha\) Cygni is representative of +a large class of stars, but it is the only one of them that has an +apparent magnitude bright enough to render it readily accessible. The +spectrum has been tabulated by Lockyer<a id="FNanchor_469" href="#Footnote_469" class="fnanchor">[469]</a> and by Wright.<a id="FNanchor_470" href="#Footnote_470" class="fnanchor">[470]</a> At the +temperatures concerned, the doubly enhanced lines of the metals are to +be anticipated, and it is probable that many of the faint unidentified +lines in the spectrum of this star are those of twice ionized metallic +atoms. The strongest doubly enhanced lines of the metals fall, as is +well known, in the ultra-violet, \(\alpha\) Cygni contains the lines of +the \(1^{2}P-3^{2}D\) series of neutral helium, the most persistent lines +of the element, and this is significant in view of the extremely low +pressure that is assigned to the atmosphere of the star on the basis of +absolute magnitude.</p> + + +<p class="nindc space-above2"> +THE <span class="allsmcap">C</span>-STARS</p> + + +<p>The c-characteristic was first used by Miss Maury<a id="FNanchor_471" href="#Footnote_471" class="fnanchor">[471]</a> to designate +stars, found in several spectral classes, that have marked spectral +peculiarities. The intensities of some of the metallic lines, chiefly +<span class="pagenum" id="Page_174">[Pg 174]</span> +those of ionized atoms, are greatly strengthened for the class, and +other lines, chiefly those of the neutral atom, are weakened. The \(G\) +band becomes markedly discontinuous, and heavy blends at 4072, 4077, +become conspicuous. The spectrum of a c-star is unmistakable in +appearance.</p> + +<h2><a id="TABLE_XXVI">TABLE XXVI</a></h2> + +<table class="autotable"> +<thead><tr> +<th class="tdc bb bt2 br">Wave<br> +Lenght</th> +<th class="tdc bb bt2 br">Wave<br> +Lenght</th> +<th class="tdc bb bt2 br"> Atom </th> +<th class="tdc bb bt2 br"> Series </th> +<th class="tdc bb bt2 br">Wave<br> +Lenght</th> +<th class="tdc bb bt2 br">Wave<br> +Lenght</th> +<th class="tdc bb bt2 br"> Atom </th> +<th class="tdc bb bt2"> Series </th> +</tr> +</thead> +<tbody><tr> +<td class="tdc br">3758.8</td> +<td class="tdc br">3757.68</td> +<td class="tdc br">Ti+</td> +<td class="tdc br">\(1^2F-1^2F'\)</td> +<td class="tdc br">4325.2</td> +<td class="tdc br">4314.98</td> +<td class="tdc br">Ti+</td> +<td class="tdc">\(1^4P-1^4D'\)</td> +</tr><tr> +<td class="tdc br"></td> +<td class="tdc br">3759.30</td> +<td class="tdc br">Ti+</td> +<td class="tdc br">\(2^2D-2^2D'\)</td> +<td class="tdc br">4321.1</td> +<td class="tdc br"></td> +<td class="tdc br">Ti+</td> +<td class="tdc"></td> +</tr><tr> +<td class="tdc br">3856.2</td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br">4337.6</td> +<td class="tdc br">4337.92</td> +<td class="tdc br">Ti+</td> +<td class="tdc">\(1^2D-1^2D'\)</td> +</tr><tr> +<td class="tdc br">3863.2</td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br">4374.7</td> +<td class="tdc br"></td> +<td class="tdc br"> Ti+?</td> +<td class="tdc"></td> +</tr><tr> +<td class="tdc br">3900.7</td> +<td class="tdc br">3900.53</td> +<td class="tdc br">Ti+</td> +<td class="tdc br">\(1^2G-1^2G'\)</td> +<td class="tdc br">4395.3</td> +<td class="tdc br">4395.04</td> +<td class="tdc br">Ti+</td> +<td class="tdc">\(1^2D-1^2F'\)</td> +</tr><tr> +<td class="tdc br">3913.6</td> +<td class="tdc br">3913.45</td> +<td class="tdc br">Ti+</td> +<td class="tdc br">\(1^2G-1^2G'\)</td> +<td class="tdc br">4400.2</td> +<td class="tdc br">4399.77</td> +<td class="tdc br">Ti+</td> +<td class="tdc">\(1^2P-1^4D'\)</td> +</tr><tr> +<td class="tdc br">4003.0</td> +<td class="tdc br">4002.09</td> +<td class="tdc br">Fe+</td> +<td class="tdc br">\(2^4P-1^4P'\)</td> +<td class="tdc br">4417.9</td> +<td class="tdc br">4417.71</td> +<td class="tdc br">Ti+</td> +<td class="tdc">\(1^4P-1^2D'\)</td> +</tr><tr> +<td class="tdc br">4009.4</td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br">4444.0</td> +<td class="tdc br">4443.80</td> +<td class="tdc br">Ti+</td> +<td class="tdc">\(1^2D-1^2F'\)</td> +</tr><tr> +<td class="tdc br">4012.6</td> +<td class="tdc br">4012.40</td> +<td class="tdc br">Ti+</td> +<td class="tdc br">\(1^2F-1^4G'\)</td> +<td class="tdc br">4450.6</td> +<td class="tdc br">4450.49</td> +<td class="tdc br">Ti+</td> +<td class="tdc">\(1^2D-1^2F'\)</td> +</tr><tr> +<td class="tdc br">4024.8</td> +<td class="tdc br">4025.13</td> +<td class="tdc br">Ti+</td> +<td class="tdc br">\(1^2F-1^4G'\)</td> +<td class="tdc br">4469.5</td> +<td class="tdc br">4468.14</td> +<td class="tdc br">Ti+</td> +<td class="tdc">\(1^2G-1^2F'\)</td> +</tr><tr> +<td class="tdc br">4028.5</td> +<td class="tdc br">4028.35</td> +<td class="tdc br">Ti+</td> +<td class="tdc br">\(2^2G-2^2F'\)</td> +<td class="tdc br">4471.8</td> +<td class="tdc br">4472.93</td> +<td class="tdc br">Fe+</td> +<td class="tdc">\(2^4F-1^4F'\)</td> +</tr><tr> +<td class="tdc br">4030.8</td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br">4409.6</td> +<td class="tdc br">4489.21</td> +<td class="tdc br">Fe+</td> +<td class="tdc">\(2^4F-1^4F'\)</td> +</tr><tr> +<td class="tdc br">4053.8</td> +<td class="tdc br">4053.84</td> +<td class="tdc br">Ti+</td> +<td class="tdc br">\(2^2G-2^2F'\)</td> +<td class="tdc br">4491.6</td> +<td class="tdc br">4491.41</td> +<td class="tdc br">Fe+</td> +<td class="tdc">\(2^4F-1^4F'\)</td> +</tr><tr> +<td class="tdc br">4077.9</td> +<td class="tdc br">4077.71</td> +<td class="tdc br">Sr+</td> +<td class="tdc br">\(1^2S-1^2P\)</td> +<td class="tdc br">4501.5</td> +<td class="tdc br">4501.27</td> +<td class="tdc br">Ti+</td> +<td class="tdc">\(1^2G-1^2F'\)</td> +</tr><tr> +<td class="tdc br">4122.8</td> +<td class="tdc br">4122.64</td> +<td class="tdc br">Fe+</td> +<td class="tdc br">\(2^4P-1^4F'\)</td> +<td class="tdc br">4508.5</td> +<td class="tdc br">4508.29</td> +<td class="tdc br">Fe+</td> +<td class="tdc">\(2^4F-1^4D'\)</td> +</tr><tr> +<td class="tdc br">4128.1</td> +<td class="tdc br">4128.</td> +<td class="tdc br">Si+</td> +<td class="tdc br"></td> +<td class="tdc br">4515.4</td> +<td class="tdc br">4515.34</td> +<td class="tdc br">Fe+</td> +<td class="tdc">\(2^4F-1^4F'\)</td> +</tr><tr> +<td class="tdc br">4131.4</td> +<td class="tdc br">4131.</td> +<td class="tdc br">Si+</td> +<td class="tdc br"></td> +<td class="tdc br">4520.3</td> +<td class="tdc br">4520.24</td> +<td class="tdc br">Fe+</td> +<td class="tdc">\(2^4F-1^4F'\)</td> +</tr><tr> +<td class="tdc br">4143.9</td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br">4522.9</td> +<td class="tdc br">4522.64</td> +<td class="tdc br">Fe+</td> +<td class="tdc">\(2^4F-1^4D'\)</td> +</tr><tr> +<td class="tdc br">4173.6</td> +<td class="tdc br">4173.47</td> +<td class="tdc br">Fe+</td> +<td class="tdc br">\(2^4P-1^4D'\)</td> +<td class="tdc br">4534.2</td> +<td class="tdc br">4533.97</td> +<td class="tdc br">Ti+</td> +<td class="tdc">\(1^2G-1^2D'\)</td> +</tr><tr> +<td class="tdc br">4179.5</td> +<td class="tdc br">4178.87</td> +<td class="tdc br">Fe+</td> +<td class="tdc br">\(2^4P-1^4F'\)</td> +<td class="tdc br"></td> +<td class="tdc br">4534.17</td> +<td class="tdc br">Fe+</td> +<td class="tdc">\(2^4F-1^4F'\)</td> +</tr><tr> +<td class="tdc br">4l87.6</td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br">4556.0</td> +<td class="tdc br">4555.90</td> +<td class="tdc br">Fe+</td> +<td class="tdc">\(2^4F-1^4F'\)</td> +</tr><tr> +<td class="tdc br">4215.7</td> +<td class="tdc br">4215.52</td> +<td class="tdc br">Sr+</td> +<td class="tdc br">\(1^2S-1^2P\)</td> +<td class="tdc br">4558.9</td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc"></td> +</tr><tr> +<td class="tdc br">4233.6</td> +<td class="tdc br">4233.16</td> +<td class="tdc br">Fe+</td> +<td class="tdc br">\(2^4P-1^4D'\)</td> +<td class="tdc br">4564.0</td> +<td class="tdc br">4563.77</td> +<td class="tdc br">Ti+</td> +<td class="tdc">\(1^2P-1^2D'\)</td> +</tr><tr> +<td class="tdc br">4271.7</td> +<td class="tdc br"></td> +<td class="tdc br"> Fe+?</td> +<td class="tdc br"></td> +<td class="tdc br">4584.0</td> +<td class="tdc br">4583.84</td> +<td class="tdc br">Fe+</td> +<td class="tdc">\(2^4F-1^4D'\)</td> +</tr><tr> +<td class="tdc br">4288.1</td> +<td class="tdc br">4287.88</td> +<td class="tdc br">Ti+</td> +<td class="tdc br">\(1^2D-1^2D'\)</td> +<td class="tdc br">4586.</td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc"></td> +</tr><tr> +<td class="tdc br">4294.3</td> +<td class="tdc br">4294.10</td> +<td class="tdc br">Ti+</td> +<td class="tdc br">\(1^2D-1^2D'\)</td> +<td class="tdc br">4619.2</td> +<td class="tdc br">4620.52</td> +<td class="tdc br">Fe+</td> +<td class="tdc">\(2^4F-1^4D'\)</td> +</tr><tr> +<td class="tdc br">4297.1</td> +<td class="tdc br">4296.56</td> +<td class="tdc br">Fe+</td> +<td class="tdc br">\(2^4P-1^4F'\)</td> +<td class="tdc br">4629.9</td> +<td class="tdc br">4629.33</td> +<td class="tdc br">Fe+</td> +<td class="tdc">\(2^4F-1^4F'\)</td> +</tr><tr> +<td class="tdc bb br">4314.4</td> +<td class="tdc bb br">4312.88?</td> +<td class="tdc bb br">Ti+</td> +<td class="tdc bb br">\(1^4P-1^4D'\)</td> +<td class="tdc bb br">4657.0</td> +<td class="tdc bb br"></td> +<td class="tdc bb br"></td> +<td class="tdc bb"></td> +</tr> + </tbody> +</table> + +<p>The foregoing tabulation contains a list of the lines that are strongly +enhanced in the spectra of the c-stars. Successive columns give the +approximate wave-length, taken from Miss Maury’s original list, the +<span class="pagenum" id="Page_175">[Pg 175]</span> +laboratory wave-length of the line with which the stellar line is +identified, the atom, and the series relations.</p> + +<p>The preponderating characteristic lines are clearly those of ionized +iron and ionized titanium.<a id="FNanchor_472" href="#Footnote_472" class="fnanchor">[472]</a> All the strong lines of these atoms are +found in the c-star spectrum, and they are there stronger than in any +other class. It is found that spectra possessing the c-character have +in general unusually sharp and narrow lines. It is probable that the +lines in the spectrum of a c-star are actually stronger, as well as +sharper, than the corresponding lines in a star of the same class and +lower luminosity.<a id="FNanchor_473" href="#Footnote_473" class="fnanchor">[473]</a></p> + +<figure class="figcenter" id="i009"> +<img src="images/i009.jpg" width="1600" height="798" alt="i009"> +<figcaption class="caption"> + +<p>Figure 9</p> + +<p>Galactic distribution of stars mentioned in the Draper Catalogue as +having narrow lines. Four sizes of dots indicate stars of different +apparent magnitudes; brighter than 5.0; 5.0-6.0; 6.0-8.0; and fainter +than 8.0, respectively.</p></figcaption> +</figure> + +<p>This phenomenon is connected with the question of the effective optical +depth of the photosphere, and is discussed in <a href="#CHAPTER_IX">Chapter IX</a>.</p> + +<p>It was first pointed out by Hertzsprung<a id="FNanchor_474" href="#Footnote_474" class="fnanchor">[474]</a> that the c-character marks +out a class of stars with distinct physical properties—extremely small +parallaxes and proper motions, strong galactic concentration, and, +accordingly, very high luminosity and volume, and low density. The +<span class="pagenum" id="Page_176">[Pg 176]</span> +last feature furnishes an interpretation of the spectral peculiarities +(see <a href="#CHAPTER_X">Chapter X</a>).</p> + +<p>The reality of the c-character has been questioned owing to a +misapprehension as to its criteria.<a id="FNanchor_475" href="#Footnote_475" class="fnanchor">[475]</a> Fine lines always accompany +the c-character, but they may be present without it. The star h Ursae +Majoris is a case in point. It is listed in the Henry Draper Catalogue +as having narrow lines, a remark that usually indicates the presence +of the c-character. Actually the star appears to be a dwarf, of Class +\(F_0\), with considerable proper motion. Although the lines are narrow +and sharp, the spectrum has not the very typical appearance of a c-star.</p> + + +<div class="footnotes"><h3>FOOTNOTES:</h3> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_439" href="#FNanchor_439" class="label">[439]</a> +E. B. Wilson and Luyten, Proc. N. Ac. Sci., 11, 133, 1925.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_440" href="#FNanchor_440" class="label">[440]</a> +J. S. Plaskett, Pub. Dom. Ap. Obs., 2, 287, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_441" href="#FNanchor_441" class="label">[441]</a> +Shapley and H. H. Wilson, H. C. 271, 1925.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_442" href="#FNanchor_442" class="label">[442]</a> +Van Maanen, Proc. N. Ac. Sci., 4, 394, 1918.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_443" href="#FNanchor_443" class="label">[443]</a> +J. S. Plaskett, Pub. Dom. Ap. Obs., 2, 147, 183, 269, 1922.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_444" href="#FNanchor_444" class="label">[444]</a> +J. S. Plaskett, Pub. Dom. Ap. Obs., 2, 287, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_445" href="#FNanchor_445" class="label">[445]</a> +Ast. and Ap., 13, 448, 1894.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_446" href="#FNanchor_446" class="label">[446]</a> +H. A. 28, 1900.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_447" href="#FNanchor_447" class="label">[447]</a> +Lick Pub., 13, 248, 1918.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_448" href="#FNanchor_448" class="label">[448]</a> +H. H. Plaskett, Pub. Dom. Ap. Obs., 1, 325, 1922.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_449" href="#FNanchor_449" class="label">[449]</a> +J. S. Plaskett, Pub. Dom. Ap. Obs., 2, 287, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_450" href="#FNanchor_450" class="label">[450]</a> +Payne, H. C. 263, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_451" href="#FNanchor_451" class="label">[451]</a> +Payne, H. C. 263, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_452" href="#FNanchor_452" class="label">[452]</a> +Preface, Henry Draper Catalogue.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_453" href="#FNanchor_453" class="label">[453]</a> +M. N. R. A. S., 83, 403, 1923.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_454" href="#FNanchor_454" class="label">[454]</a> +H. C. 258, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_455" href="#FNanchor_455" class="label">[455]</a> +Chapter IV, <a href="#Page_52">p. 52</a>.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_456" href="#FNanchor_456" class="label">[456]</a> +Shapley, H. B. 805, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_457" href="#FNanchor_457" class="label">[457]</a> +Shapley, Rep. Spectr. Class. Com., I. A. U., 1925.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_458" href="#FNanchor_458" class="label">[458]</a> +See <a href="#APPENDICES">Appendix</a>.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_459" href="#FNanchor_459" class="label">[459]</a> +Mt. W. Contr. 244, 1922; 262, 1923.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_460" href="#FNanchor_460" class="label">[460]</a> +H. C. 264, 1924; cf. Lindblad, Ap. J., 59, 305, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_461" href="#FNanchor_461" class="label">[461]</a> +Shapley, H. B. 798, 1924; Luyten, H. C. 251, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_462" href="#FNanchor_462" class="label">[462]</a> +Rep. Spectr. Class. Com., I. A. U., 1922.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_463" href="#FNanchor_463" class="label">[463]</a> +Luyten, H. B. 797, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_464" href="#FNanchor_464" class="label">[464]</a> +J. S. Plaskett, Pub. Dom. Ap. Obs., 2, 335, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_465" href="#FNanchor_465" class="label">[465]</a> +Lockyer and Baxandall, Proc. Roy. Soc., 77A, 550, 1906.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_466" href="#FNanchor_466" class="label">[466]</a> +Belopolsky, Pub. Ac. Imp. St. Pet., 6, 12, 1913; Pulk. Bul., 6, +10, 1915.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_467" href="#FNanchor_467" class="label">[467]</a> +Lockyer and Baxandall, Proc. Roy. Soc., 77A, 550, 1906.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_468" href="#FNanchor_468" class="label">[468]</a> +Kiess, Pub. Obs. Mich., 3, 106, 1923.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_469" href="#FNanchor_469" class="label">[469]</a> +Lockyer, Pub. Sol. Phys. Com., 1904.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_470" href="#FNanchor_470" class="label">[470]</a> +Wright, L. O. B. 332, 1921.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_471" href="#FNanchor_471" class="label">[471]</a> +A. C. Maury, H. A., 28, 79, 1897.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_472" href="#FNanchor_472" class="label">[472]</a> +Russell, Ap. J., in press.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_473" href="#FNanchor_473" class="label">[473]</a> +Stewart, Phys. Rev., 22, 324, 1923; Russell and Stewart, +Ap. J., 59, 197, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_474" href="#FNanchor_474" class="label">[474]</a> +A. N., 179, 374, 1908; A. N., 192, 262, 1912.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_475" href="#FNanchor_475" class="label">[475]</a> +Harper and Young, J. R. A. S. Can., 18, 9, 1924.</p> + +</div> +</div> + +<hr class="chap x-ebookmaker-drop"> + +<div class="chapter"> +<p><span class="pagenum" id="Page_177">[Pg 177]</span></p> + +<h2 class="nobreak" id="CHAPTER_XIII">CHAPTER XIII<br> +THE RELATIVE ABUNDANCE OF THE ELEMENTS</h2> +</div> + +<p class="nind"> +THE relative frequency of atomic species has for some time been of +recognized significance. Numerous deductions have been based upon +the observed terrestrial distribution of the elements; for example, +attention has been drawn to the preponderance of the lighter elements +(comprising those of atomic number less than thirty), to the “law of +even numbers,” which states that elements of even atomic number are +far more frequent than elements of odd atomic number, and to the high +frequency of atoms with an atomic weight that is a multiple of four.</p> + +<p>The existence of these general relations for the atoms that occur in +the crust of the earth is in itself a fact of the highest interest, +but the considerations contained in the present chapter indicate that +such relations also hold for the atoms that constitute the stellar +atmospheres and therefore have an even deeper significance than was at +first supposed. Data on the subject of the relative frequency of the +different species of atoms contain a possible key to the problem of +the evolution and stability of the elements. Though the time does not +as yet seem ripe for an interpretation of the facts, the collection of +data on a comprehensive scale will prepare the way for theory, and will +help to place it, when it comes, on a sound observational basis.</p> + +<p>The intensity of the absorption lines associated with an element +immediately suggests itself as a possible source of information +on relative abundance. But the same species of atom gives rise +simultaneously to lines of different intensities belonging to the +same series, and also to different series, which change in intensity +relative to one another according to the temperature of the star. The +intensity of the absorption line is, of course, a very complex function +of the temperature, the pressure, and the atomic constants—a matter +<span class="pagenum" id="Page_178">[Pg 178]</span> +that has been discussed in detail in the preceding seven chapters.</p> + +<p>The observed intensity can therefore be used directly for only a +crude estimate of abundance. Roughly speaking, the lines of the +lighter elements predominate in the spectra of stellar atmospheres, +and probably the corresponding atoms constitute the greater part of +the atmosphere of the star, as they do of the earth’s crust. Beyond a +general inference such as this, few direct conclusions can be drawn +from line-intensities. Russell<a id="FNanchor_476" href="#Footnote_476" class="fnanchor">[476]</a> made the solar spectrum the basis +of a discussion in which he pointed out the apparent similarity in +composition between the crust of the earth, the atmosphere of the star, +and the meteorites of the stony variety. The method used by him should +be expected, in the light of subsequent work, to yield only qualitative +results, since it took no account of the relative probabilities of the +atomic states corresponding to different lines in the spectrum.</p> + + +<p class="nindc space-above2"> +UNIFORMITY OF COMPOSITION OF THE STELLAR ATMOSPHERE</p> + + +<p>The possibility of arranging the majority of stellar spectra in +homogeneous classes that constitute a continuous series, is an +indication that the composition of the stars is remarkably uniform—at +least in regard to the portion that can be examined spectroscopically. +The fact that so many stars have <i>identical</i> spectra is in itself +a fact suggesting uniformity of composition; and the success of the +theory of thermal ionization in predicting the spectral changes that +occur from class to class is a further indication in the same direction.</p> + +<p>If departures from uniform distribution did occur from one class to +another, they might conceivably be masked by the thermal changes of +intensity. But it is exceedingly improbable that a lack of uniformity +in distribution would in every case be thus concealed. It is also +unlikely, though possible, that a departure from uniformity would +affect equally and solely the stars of one spectral class. Any such +departure, if found, would indicate that the presence of abnormal +quantities of certain elements was an effect of temperature. This +<span class="pagenum" id="Page_179">[Pg 179]</span> +explanation appears, however, to be neither justified nor necessary; +there is no reason to assume a sensible departure from uniform +composition for members of the normal stellar sequence.</p> + + +<p class="nindc space-above2"> +MARGINAL APPEARANCE OF SPECTRUM LINES</p> + + +<p>Fowler and Milne<a id="FNanchor_477" href="#Footnote_477" class="fnanchor">[477]</a> pointed out that the “marginal appearance,” when +the line is at the limit of visibility, is a function of the abundance +of the corresponding atom. For this reason their own theory, which +dealt not with the marginal appearance but with the maximum of an +absorption line, was capable of a more satisfactory observational test +than Saha’s. It is possible, as shown below, to extend the Fowler-Milne +considerations and to use the observed marginal appearances as a +measure of relative abundance.</p> + +<p>The conditions for marginal appearance must first be formulated. +When a strong absorption line is at maximum, the light received from +its center comes from the deepest layer that is possible for the +corresponding frequency. The actual depth depends, as was pointed out +in <a href="#CHAPTER_IX">Chapter IX</a>, upon the number of absorbing atoms per unit volume, and +upon the atomic absorption coefficient for the frequency in question. +The suggestions that were put forward in the chapter just quoted +indicate that different lines, at their maxima, arise from different +“effective levels,” the more abundant atoms appearing, other things +being equal, at higher levels.</p> + +<p>As an absorption line is traced through the classes adjacent to the one +at which it attains maximum, it begins to diminish in intensity, owing +to the decrease in the number of suitable atoms. If the line is very +intense, the first effect of the fall in the number of suitable atoms +is a reduction in the width and wings. As the number of suitable atoms +per unit volume decreases further, a greater and greater thickness of +atmosphere is required to produce the same amount of absorption, and +accordingly the line originates deeper and deeper in the atmosphere +of the star. As the “effective level” falls, the temperature of the +<span class="pagenum" id="Page_180">[Pg 180]</span> +layer that gives rise to the line increases, owing to the temperature +gradient in the stellar reversing layer. The observed fall in the +intensity of the line is caused both by the reduction in the number of +suitable atoms, and by the decreased contrast between the line and the +background. The former cause predominates for strong (saturated) lines, +and the latter for weak (unsaturated) lines.</p> + +<p>As the atoms suitable to the absorption of the line considered decrease +in number, the effective level from which the line takes its origin +falls, and ultimately coincides with the photosphere (the level at +which the <i>general</i> absorption becomes great enough to mask +the <i>selective</i> absorption due to individual atoms). The line +then disappears owing to lack of contrast. Immediately before the +line merges into the photosphere (the approximate point estimated +as “marginal appearance”), <i>all</i> the suitable atoms above the +photosphere are clearly contributing to the absorption; in other +words the <i>line</i> is unsaturated. The position in the spectral +sequence of the marginal appearance of a line must then depend directly +.upon the <i>number of suitable atoms above the photosphere</i>; +considerations of effective level are eliminated. Hence a constant +\(P_e\) is used on <a href="#Page_184">page 184</a>.</p> + +<p>The conditions at maximum and marginal appearance of a line in the +spectral sequence are to some extent reproduced for an individual +absorption line at the center of the line and at the edge of its wing. +A hydrogen line displays wings that may extend to thirty Angstrom +units on either side of the center. The energy contributing to the +wings is evidently light coming from hydrogen atoms with a frequency +that deviates somewhat from the normal. Atoms with small deviations +are more numerous than atoms with large deviations, and therefore the +light received from them originates in a higher effective level. The +line center corresponds to the highest level of all. At points far +out upon the wings, lower and lower levels are represented, until, +where the line merges into the continuous background, the level from +which it originates coincides with the photosphere, and the “marginal +<span class="pagenum" id="Page_181">[Pg 181]</span> +appearance” of the line (if it may so be called) is reached. Accurate +photometry of the centers and wings of strong absorption lines would +seem to have an important bearing on the structure of the stellar +atmosphere, as it would provide an immediate measure of the factor that +produces the deviations from normal frequency. The success of parallel +work in the laboratory<a id="FNanchor_478" href="#Footnote_478" class="fnanchor">[478]</a> indicates that intensity distribution +should be amenable to observation and to theory.</p> + + +<p class="nindc space-above2"> +OBSERVED MARGINAL APPEARANCES</p> + + +<p>The spectral class at which a line is first or last seen is obviously, +to some extent, a function of the spectroscopic dispersion used, for, +with extremely small dispersion, many of the fainter lines fail to +appear at all. A line will also probably appear somewhat later, and +disappear somewhat earlier, with small than with large dispersion. +It is therefore a matter of some difficulty to obtain measures of +marginal appearance that shall be absolute, but the present discussion +neither assumes nor requires them. The method used is designed for the +estimation of relative abundances, and all that is required of the data +is that they shall be mutually consistent.</p> + +<p>In order to attain the maximum degree of consistency, the estimates +used in this chapter were derived chiefly from the two series of +plates mentioned in <a href="#CHAPTER_VIII">Chapter VIII</a>. All the plates used were made with +the same dispersion (two 150 objective prisms) and were of comparable +density, and of good definition. The data furnished by the writer’s own +measures were supplemented by some estimates derived by Menzel<a id="FNanchor_479" href="#Footnote_479" class="fnanchor">[479]</a> +from a similar series of plates, of the same dispersion and comparable +quality. The estimate of the marginal appearance of potassium was very +kindly suggested by Russell from solar observations.</p> + +<p>The observed marginal appearances of all the lines that are available +are summarized in the table that follows. Successive columns contain +the atomic number and atom, the series relations, the wave-length of +the line used, and the Draper classes at which the line is observed, +<span class="pagenum" id="Page_182">[Pg 182]</span> +respectively, to appear, to reach maximum, and to disappear. Asterisks +in the last column denote the ultimate lines of the neutral atom, which +are strongest at low temperatures, and have no maximum.</p> + +<h2><a id="TABLE_XXVII">TABLE XXVII</a></h2> +<table class="autotable"> +<thead><tr> +<th class="tdc bb bt2 br" colspan="2">Atom</th> +<th class="tdc bb bt2 br"> Series </th> +<th class="tdc bb bt2 br"> Line </th> +<th class="tdc bb bt2 br" colspan="3"> Classes </th> +<th class="tdc bb bt2 br" colspan="2">Atom</th> +<th class="tdc bb bt2 br"> Series </th> +<th class="tdc bb bt2 br"> Line </th> +<th class="tdc bb bt2" colspan="3"> Classes </th> +</tr> +</thead> +<tbody><tr> +<td class="tdl">1</td> +<td class="tdl br">H</td> +<td class="tdc br">\(1S-2P\)</td> +<td class="tdc br">4340</td> +<td class="tdl">-</td> +<td class="tdc">\(A_3\)</td> +<td class="tdr br">-</td> +<td class="tdl">22</td> +<td class="tdl br">Ti</td> +<td class="tdc br">\(_1F-F\)</td> +<td class="tdc br">3999</td> +<td class="tdl">*</td> +<td class="tdc">*</td> +<td class="tdr">\(A_2\)</td> +</tr><tr> +<td class="tdl">2</td> +<td class="tdl br">He</td> +<td class="tdc br">\(1^2P-3^2D\)</td> +<td class="tdc br">4471</td> +<td class="tdl">\(B_9\)</td> +<td class="tdc">\(B_3\)</td> +<td class="tdr br">\(O\)</td> +<td class="tdl"></td> +<td class="tdl br"></td> +<td class="tdc br">\(_1F-G\)</td> +<td class="tdc br">4862</td> +<td class="tdl">*</td> +<td class="tdc">*</td> +<td class="tdr">\(A_2\)</td> +</tr><tr> +<td class="tdl"></td> +<td class="tdl br"></td> +<td class="tdc br">\(_1S-_2P\)</td> +<td class="tdc br">5015</td> +<td class="tdl">\(B_9\)</td> +<td class="tdc">\(B_3\)</td> +<td class="tdr br">\(O\)</td> +<td class="tdl"></td> +<td class="tdl br"></td> +<td class="tdl br"></td> +<td class="tdc br">4867</td> +<td class="tdl">*</td> +<td class="tdc">*</td> +<td class="tdr">\(A_2\)</td> +</tr><tr> +<td class="tdl"></td> +<td class="tdl br"></td> +<td class="tdc br">\(_1P-_4D\)</td> +<td class="tdc br">4388</td> +<td class="tdl">\(B_9\)</td> +<td class="tdc">\(B_3\)</td> +<td class="tdr br">\(O\)</td> +<td class="tdl"></td> +<td class="tdl br"></td> +<td class="tdl br"></td> +<td class="tdc br">4856</td> +<td class="tdl">*</td> +<td class="tdc">*</td> +<td class="tdr">\(A_2\)</td> +</tr><tr> +<td class="tdl"></td> +<td class="tdl br">He+</td> +<td class="tdc br">\(-_4F-9G\)</td> +<td class="tdc br">4542</td> +<td class="tdl">\(O\)</td> +<td class="tdc">\(O\)</td> +<td class="tdr br">-</td> +<td class="tdl"></td> +<td class="tdl br"></td> +<td class="tdc br">\(1^5F-^5F\)</td> +<td class="tdc br">4536</td> +<td class="tdl">-</td> +<td class="tdc">-</td> +<td class="tdr">\(A_5\)</td> +</tr><tr> +<td class="tdl">3</td> +<td class="tdl br">Li</td> +<td class="tdc br">\(1^2S-1^2P\)</td> +<td class="tdc br">6707</td> +<td class="tdl">*</td> +<td class="tdc">*</td> +<td class="tdr br">-</td> +<td class="tdl"></td> +<td class="tdl br"></td> +<td class="tdl br"></td> +<td class="tdc br">4535</td> +<td class="tdl">-</td> +<td class="tdc">-</td> +<td class="tdr">\(A_5\)</td> +</tr><tr> +<td class="tdl">6</td> +<td class="tdl br">C+</td> +<td class="tdc br">\(2^2D-3^2F\)</td> +<td class="tdc br">4267</td> +<td class="tdl">\(B_9\)</td> +<td class="tdc">\(B_3\)</td> +<td class="tdr br">\(O\)</td> +<td class="tdl">23</td> +<td class="tdl br">V</td> +<td class="tdc br">\(1^6G-^6G\)</td> +<td class="tdc br">4333</td> +<td class="tdl">*</td> +<td class="tdc">*</td> +<td class="tdr">\(F_0\)</td> +</tr><tr> +<td class="tdl">11</td> +<td class="tdl br">Na</td> +<td class="tdc br">\(1^2S-1^2P\)</td> +<td class="tdc br">5889</td> +<td class="tdl">*</td> +<td class="tdc">*</td> +<td class="tdr br">\(A_0 \ddagger\)</td> +<td class="tdl"></td> +<td class="tdl br"></td> +<td class="tdl br"></td> +<td class="tdc br">4330</td> +<td class="tdl">*</td> +<td class="tdc">*</td> +<td class="tdr">\(F_0\)</td> +</tr><tr> +<td class="tdl"></td> +<td class="tdl br"></td> +<td class="tdc br"></td> +<td class="tdc br">5896</td> +<td class="tdl">*</td> +<td class="tdc">*</td> +<td class="tdr br">\(A_0 \ddagger\)</td> +<td class="tdl">24</td> +<td class="tdl br">Cr</td> +<td class="tdc br">\(1^7S-1^7P\)</td> +<td class="tdc br">4290</td> +<td class="tdl">*</td> +<td class="tdc">*</td> +<td class="tdr">\(A_2\)</td> +</tr><tr> +<td class="tdl">12</td> +<td class="tdl br">Mg</td> +<td class="tdc br">\(1^3P-1^3D\)</td> +<td class="tdc br">5184</td> +<td class="tdl">-</td> +<td class="tdc">?</td> +<td class="tdr br">\(A_0 \ddagger\)</td> +<td class="tdl"></td> +<td class="tdl br"></td> +<td class="tdl br"></td> +<td class="tdc br">4275</td> +<td class="tdl">*</td> +<td class="tdc">*</td> +<td class="tdr">\(A_2\)</td> +</tr><tr> +<td class="tdl"></td> +<td class="tdl br"></td> +<td class="tdc br"></td> +<td class="tdc br">5173</td> +<td class="tdl">-</td> +<td class="tdc">?</td> +<td class="tdr br">\(A_0 \ddagger\)</td> +<td class="tdl"></td> +<td class="tdl br"></td> +<td class="tdl br"></td> +<td class="tdc br">4254</td> +<td class="tdl">*</td> +<td class="tdc">*</td> +<td class="tdr">\(A_2\)</td> +</tr><tr> +<td class="tdl"></td> +<td class="tdl br"></td> +<td class="tdc br"></td> +<td class="tdc br">5167</td> +<td class="tdl">-</td> +<td class="tdc">?</td> +<td class="tdr br">\(A_0 \ddagger\)</td> +<td class="tdl"></td> +<td class="tdl br"></td> +<td class="tdc br">\(1^5S-1^5P\)</td> +<td class="tdc br">4497</td> +<td class="tdl">-</td> +<td class="tdc">\(M_1\)</td> +<td class="tdr">\(A_7\)</td> +</tr><tr> +<td class="tdl"></td> +<td class="tdl br"></td> +<td class="tdc br">\(1^3P-2^3D\)</td> +<td class="tdc br">3838</td> +<td class="tdl">-</td> +<td class="tdc">?</td> +<td class="tdr br">\(A_0\)</td> +<td class="tdl">25</td> +<td class="tdl br">Mn</td> +<td class="tdc br">\(1^6S-1^6P\)</td> +<td class="tdc br">4034</td> +<td class="tdl">*</td> +<td class="tdc">*</td> +<td class="tdr">\(A_2\)</td> +</tr><tr> +<td class="tdl"></td> +<td class="tdl br"></td> +<td class="tdc br"></td> +<td class="tdc br">3832</td> +<td class="tdl">-</td> +<td class="tdc">?</td> +<td class="tdr br">\(A_0\)</td> +<td class="tdl"></td> +<td class="tdl br"></td> +<td class="tdl br"></td> +<td class="tdc br">4033</td> +<td class="tdl">*</td> +<td class="tdc">*</td> +<td class="tdr">\(A_2\)</td> +</tr><tr> +<td class="tdl"></td> +<td class="tdl br"></td> +<td class="tdc br"></td> +<td class="tdc br">3829</td> +<td class="tdl">-</td> +<td class="tdc">?</td> +<td class="tdr br">\(A_0\)</td> +<td class="tdl"></td> +<td class="tdl br"></td> +<td class="tdl br"></td> +<td class="tdc br">4030</td> +<td class="tdl">*</td> +<td class="tdc">*</td> +<td class="tdr">\(A_2\)</td> +</tr><tr> +<td class="tdl"></td> +<td class="tdl br">Mg+</td> +<td class="tdc br">\(2^3D-3^2F\)</td> +<td class="tdc br">4481</td> +<td class="tdl">-</td> +<td class="tdc">\(A_3\)</td> +<td class="tdr br">\(B_O\)</td> +<td class="tdl"></td> +<td class="tdl br"></td> +<td class="tdc br">\(1^6D-^6D\)</td> +<td class="tdc br">4084</td> +<td class="tdl">-</td> +<td class="tdc">\(K_2\)</td> +<td class="tdr">\(A_3\)</td> +</tr><tr> +<td class="tdl">13</td> +<td class="tdl br">Al</td> +<td class="tdc br">\(1^2P-1^2S\)</td> +<td class="tdc br">3962</td> +<td class="tdl">*</td> +<td class="tdc">*</td> +<td class="tdr br">\(A_O\)</td> +<td class="tdl"></td> +<td class="tdl br"></td> +<td class="tdl br"></td> +<td class="tdc br">4041</td> +<td class="tdl">-</td> +<td class="tdc">\(K_2\)</td> +<td class="tdr">\(A_3\)</td> +</tr><tr> +<td class="tdl"></td> +<td class="tdl br"></td> +<td class="tdc br"></td> +<td class="tdc br">3944</td> +<td class="tdl">*</td> +<td class="tdc">*</td> +<td class="tdr br">\(A_O\)</td> +<td class="tdl">26</td> +<td class="tdl br">Fe</td> +<td class="tdc br">\(1^3F-^3G\)</td> +<td class="tdc br">4325</td> +<td class="tdl">-</td> +<td class="tdc">\(K_2\)</td> +<td class="tdr">\(A_2\)</td> +</tr><tr> +<td class="tdl">14</td> +<td class="tdl br">Si</td> +<td class="tdc br"></td> +<td class="tdc br">3905</td> +<td class="tdl">-</td> +<td class="tdc">\(G_0\)</td> +<td class="tdr br">\(A_2\)</td> +<td class="tdl"></td> +<td class="tdl br"></td> +<td class="tdc br">\(1^3F-^3F\)</td> +<td class="tdc br">4811</td> +<td class="tdl">\(G_5\)</td> +<td class="tdc">\(G_0\)</td> +<td class="tdr">\(A_7 \dagger\)</td> +</tr><tr> +<td class="tdl"></td> +<td class="tdl br">Si+</td> +<td class="tdc br"></td> +<td class="tdc br">4128</td> +<td class="tdl">\(F_0\)</td> +<td class="tdc">\(A_0\)</td> +<td class="tdr br">\(O\)</td> +<td class="tdl">30</td> +<td class="tdl br">Zn</td> +<td class="tdc br">\(1^3P-1^3S\)</td> +<td class="tdc br">4811</td> +<td class="tdl">\(G_5\)</td> +<td class="tdc">\(G_0\)</td> +<td class="tdr">\(A_7 \dagger\)</td> +</tr><tr> +<td class="tdl"></td> +<td class="tdl br"></td> +<td class="tdc br"></td> +<td class="tdc br">4131</td> +<td class="tdl">\(F_0\)</td> +<td class="tdc">\(A_0\)</td> +<td class="tdr br">\(O\)</td> +<td class="tdl"></td> +<td class="tdl br"></td> +<td class="tdl br"></td> +<td class="tdc br">4722</td> +<td class="tdl">\(G_5\)</td> +<td class="tdc">\(G_0\)</td> +<td class="tdr">\(A_7 \dagger\)</td> +</tr><tr> +<td class="tdl">19</td> +<td class="tdl br">K</td> +<td class="tdc br">\(1^2S-1^2P\)</td> +<td class="tdc br">4044</td> +<td class="tdl">*</td> +<td class="tdc">*</td> +<td class="tdr br">\(F_8\)</td> +<td class="tdl">38</td> +<td class="tdl br">Sr</td> +<td class="tdc br">\(_1S-_1P\)</td> +<td class="tdc br">4607</td> +<td class="tdl">*</td> +<td class="tdc">*</td> +<td class="tdr">\(F_0\)</td> +</tr><tr> +<td class="tdl"></td> +<td class="tdl br"></td> +<td class="tdc br"></td> +<td class="tdc br">4047</td> +<td class="tdl">*</td> +<td class="tdc">*</td> +<td class="tdr br">\(F_8\)</td> +<td class="tdl"></td> +<td class="tdl br">Sr+</td> +<td class="tdc br">\(1^2S-1^2D\)</td> +<td class="tdc br">4078</td> +<td class="tdl">-</td> +<td class="tdc">\(K_2\)</td> +<td class="tdr">\(A_0\)</td> +</tr><tr> +<td class="tdl">20</td> +<td class="tdl br">Ca</td> +<td class="tdc br">\(_1S-_1P\)</td> +<td class="tdc br">4227</td> +<td class="tdl">*</td> +<td class="tdc">*</td> +<td class="tdr br">\(B_9\)</td> +<td class="tdl">54</td> +<td class="tdl br">Ba+</td> +<td class="tdc br">\(1^2S-1^2P\)</td> +<td class="tdc br">4555</td> +<td class="tdl">-</td> +<td class="tdc">?</td> +<td class="tdr">\(A_2\)</td> +</tr><tr> +<td class="tdl"></td> +<td class="tdl br"></td> +<td class="tdc br">\(1^3P-2^3D\)</td> +<td class="tdc br">4455</td> +<td class="tdl">-</td> +<td class="tdc">\(K_2\)</td> +<td class="tdr br">\(F_0\)</td> +<td class="tdl"></td> +<td class="tdl br"></td> +<td class="tdl br"></td> +<td class="tdc br"></td> +<td class="tdl"></td> +<td class="tdc"></td> +<td class="tdr"></td> +</tr><tr> +<td class="tdl bb"></td> +<td class="tdl bb br">Ca+</td> +<td class="tdc bb br">\(1^2S-1^2P\)</td> +<td class="tdc bb br">3933</td> +<td class="tdl bb">-</td> +<td class="tdc bb">-</td> +<td class="tdr bb br">\(B_0\)</td> +<td class="tdl bb"></td> +<td class="tdl bb br"></td> +<td class="tdl bb br"></td> +<td class="tdc bb br"></td> +<td class="tdl bb"></td> +<td class="tdc bb"></td> +<td class="tdr bb"></td> +</tr> + </tbody> +</table> + +<p><span class="pagenum" id="Page_183">[Pg 183]</span></p> + +<p>Estimates by Menzel are indicated by a dagger; those marked by a +double dagger were taken from dyed plates made with slightly smaller +dispersion.</p> + + +<p class="nindc space-above2"> +METHOD OF ESTIMATING RELATIVE ABUNDANCES</p> + + +<p>If the physical conception of marginal appearance above outlined +is correct, the <i>number of atoms</i> of a given kind above the +photosphere will practically determine the class at which the +corresponding line is last seen.<a id="FNanchor_480" href="#Footnote_480" class="fnanchor">[480]</a> Now at marginal appearance the +number of suitable atoms is only a small fraction of the total amount +of the corresponding element that is present in the reversing layer, +and this fraction is precisely the “fractional concentration” evaluated +by Fowler and Milne. If then it be assumed that the number of atoms +required for marginal appearance is the same for all elements, the +reciprocals of the computed fractional concentrations at marginal +appearance should give directly the relative abundances of the atoms.</p> + +<p>A few remarks concerning the underlying assumptions may be appropriate. +In applying the theory it is assumed that stellar atmospheres are of +uniform composition, and that at marginal appearance all lines are +unsaturated. These reasonable assumptions have been discussed above, +and they are here explicitly restated. The third assumption, that +the same number of atoms is represented at the marginal appearance +of a line, whatever the element, is by far the most serious. It +implies the equality of the absorbing efficiencies of the individual +atoms under the conditions involved. This is assumed in default of a +suitable correction, but it is not suggested that the use here made +of the assumption would imply its universal validity. Its present +application is made under conditions of extremely low pressure +(\(\displaystyle{1.31~\times~ 10^{-4}~ \text{atmospheres}}\)), +and over a range of temperature from 7000° to 10,000°. Under such +conditions the absorbing efficiency of an atom will depend almost +entirely upon its energy supply and upon its inherent tendency to +recover after undergoing an electron transfer. The pressures are so +low that collisions will have no appreciable effect in disturbing +the normal recovery of the atoms. The energy supply will vary with +the temperature; but with the range of temperature considered the +<span class="pagenum" id="Page_184">[Pg 184]</span> +variation will probably not be very large. The reorganization time +of an atom appears to be an atomic constant, and to be of the same +order for all atoms hitherto examined in the laboratory or in stellar +atmospheres. As a working assumption, then, the equality of the +atomic absorption coefficients is assumed with some confidence in the +discussion of observed marginal appearances.</p> + +<h2><a id="TABLE_XXVIII">TABLE XXVIII</a></h2> + +<table class="autotable"> +<thead><tr> +<th class="tdc">Atomic Number</th> +<th class="tdc_ws1">Atom</th> +<th class="tdc_ws1">\(\log \sigma_r\)</th> +<th class="tdc">Atomic Number</th> +<th class="tdc_ws1">Atom</th> +<th class="tdc_ws1">\(\log \sigma_r\)</th> +<th class="tdc">Atomic Number</th> +<th class="tdc_ws1">Atom</th> +<th class="tdc_ws1">\(\log \sigma_r\)</th> +</tr> +</thead> +<tbody><tr> +<td class="tdc">1</td> +<td class="tdl">H</td> +<td class="tdc">11</td> +<td class="tdc">13</td> +<td class="tdl">Al</td> +<td class="tdc">5.0</td> +<td class="tdc">23</td> +<td class="tdl">V</td> +<td class="tdc">3.0</td> +</tr><tr> +<td class="tdc">2</td> +<td class="tdl">He</td> +<td class="tdc">8.3</td> +<td class="tdc">14</td> +<td class="tdl">Si</td> +<td class="tdc">4.8</td> +<td class="tdc">24</td> +<td class="tdl">Cr</td> +<td class="tdc">3.9</td> +</tr><tr> +<td class="tdc"></td> +<td class="tdl">He+</td> +<td class="tdc">12</td> +<td class="tdc"></td> +<td class="tdl">Si+</td> +<td class="tdc">4.9</td> +<td class="tdc">25</td> +<td class="tdl">Mn</td> +<td class="tdc">4.6</td> +</tr><tr> +<td class="tdc">3</td> +<td class="tdl">Li</td> +<td class="tdc">0.0</td> +<td class="tdc"></td> +<td class="tdl">Si+++</td> +<td class="tdc">6.0</td> +<td class="tdc">26</td> +<td class="tdl">Fe</td> +<td class="tdc">4.8</td> +</tr><tr> +<td class="tdc">6</td> +<td class="tdl">C+</td> +<td class="tdc">4.5</td> +<td class="tdc">19</td> +<td class="tdl">K</td> +<td class="tdc">3.5</td> +<td class="tdc">30</td> +<td class="tdl">Zn</td> +<td class="tdc">4.2</td> +</tr><tr> +<td class="tdc">11</td> +<td class="tdl">Na</td> +<td class="tdc">5.2</td> +<td class="tdc">20</td> +<td class="tdl">Ca</td> +<td class="tdc">4.8</td> +<td class="tdc">38</td> +<td class="tdl">Sr</td> +<td class="tdc">1.8</td> +</tr><tr> +<td class="tdc">12</td> +<td class="tdl">Mg</td> +<td class="tdc">5.6</td> +<td class="tdc"></td> +<td class="tdl">Ca+</td> +<td class="tdc">5.0</td> +<td class="tdc"></td> +<td class="tdl">Sr+</td> +<td class="tdc">1.5</td> +</tr><tr> +<td class="tdc"></td> +<td class="tdl">Mg+</td> +<td class="tdc">5.5</td> +<td class="tdc">22</td> +<td class="tdl">Ti</td> +<td class="tdc">4.1</td> +<td class="tdc">54</td> +<td class="tdl">Ba+</td> +<td class="tdc">1.1</td> +</tr> + </tbody> +</table> + +<p>As stated above, the relative abundances of the atoms are given +directly by the reciprocals of the respective fractional concentrations +at marginal appearance. The values of the relative abundance thus +deduced are contained in <a href="#TABLE_XXVIII">Table XXVIII</a>. Successive columns give the +atomic number, the atom, and the logarithm of the relative abundance, +\(a_r\).</p> + + +<p class="nindc space-above2"> +COMPARISON OF STELLAR ATMOSPHERE AND EARTH'S CRUST</p> + + +<p>The preponderance of the lighter elements in stellar atmospheres is +a striking aspect of the results, and recalls the similar feature +that is conspicuous in analyses of the crust of the earth.<a id="FNanchor_481" href="#Footnote_481" class="fnanchor">[481]</a> A +distinct parallelism in the relative frequencies of the atoms of the +more abundant elements in both sources has already been suggested by +Russell,<a id="FNanchor_482" href="#Footnote_482" class="fnanchor">[482]</a> and discussed by H. H. Plaskett,<a id="FNanchor_483" href="#Footnote_483" class="fnanchor">[483]</a> +<span class="pagenum" id="Page_185">[Pg 185]</span> +and the data contained in <a href="#TABLE_XXVIII">Table XXVIII</a> confirm +and amplify the similarity.</p> + +<p>A close correspondence between the percentage compositions of the +stellar atmosphere and the crust of the earth would not, perhaps, +be expected, since both sources form a negligible fraction of the +body of which they are a part. There is every reason to suppose, +on observational and theoretical grounds, that the composition of +the earth varies with depth below the surface; and the theory of +thermodynamical equilibrium would appear to lead to the result that +the heavier atoms should, on the average, gravitate to the center of a +star. If, however, the earth originated from the surface layers of the +sun,<a id="FNanchor_484" href="#Footnote_484" class="fnanchor">[484]</a> the percentage composition of the whole earth should resemble +the composition of the solar (and therefore of a typical stellar) +atmosphere. But the mass of the earth alone is considerably in excess +of the mass of the reversing layer of the sun.<a id="FNanchor_485" href="#Footnote_485" class="fnanchor">[485]</a> Eddington,<a id="FNanchor_486" href="#Footnote_486" class="fnanchor">[486]</a> +quoting von Zeipel,<a id="FNanchor_487" href="#Footnote_487" class="fnanchor">[487]</a> has pointed out that an effect of rotation of +a star will be to keep the constituents well mixed, so that the outer +portions of the sun or of a star are probably fairly representative of +the interior. Considering the possibility of atomic segregation both in +the earth and in the star, it appears likely that the earth’s crust is +representative of the stellar atmosphere.</p> + +<p>The most obvious conclusion that can be drawn from <a href="#TABLE_XXVIII">Table XXVIII</a> is +that all the commoner elements found terrestrially, which could also, +for spectroscopic reasons, be looked for in the stellar atmosphere, +are actually observed in the stars. The twenty-four elements that are +commonest in the crust of the earth,<a id="FNanchor_488" href="#Footnote_488" class="fnanchor">[488]</a> in order of atomic abundance, +are oxygen, silicon, hydrogen, aluminum, sodium, calcium, iron, +magnesium, potassium, titanium, carbon, chlorine, phosphorus, sulphur, +nitrogen, manganese, fluorine, chromium, vanadium, lithium, barium, +zirconium, nickel, and strontium.</p> + +<p>The most abundant elements found in stellar atmospheres, also in +<span class="pagenum" id="Page_186">[Pg 186]</span> +order of abundance, are silicon, sodium, magnesium, aluminum, carbon, +calcium, iron, zinc, titanium, manganese, chromium, potassium, +vanadium, strontium, barium, (hydrogen, and helium). All the atoms for +which quantitative estimates have been made are included in this list. +Although hydrogen and helium are manifestly very abundant in stellar +atmospheres, the actual values derived from the estimates of marginal +appearance are regarded as spurious.</p> + +<p>The absence from the stellar list of eight terrestrially abundant +elements can be fully accounted for. The substances in question are +oxygen, chlorine, phosphorus, sulphur, nitrogen, fluorine, zirconium, +and nickel, and none of these elements gives lines of known series +relations in the region ordinarily photographed.</p> + +<p>The \(1^{5}S-m^{5}P\) “triplets” of neutral oxygen, in the red, should +prove accessible in the near future; the point of disappearance of +these lines would not be difficult to estimate, and they would furnish +a value for the stellar abundance of oxygen. The lines of ionized +oxygen, which have not yet been analyzed into series, are conspicuous +in the \(B\) stars,<a id="FNanchor_489" href="#Footnote_489" class="fnanchor">[489]</a> and the element is probably present in large +quantities.</p> + +<p>Sulphur and nitrogen both lack suitable lines in the region usually +studied; the analyzed spectrum of neutral sulphur is in the green and +red,<a id="FNanchor_490" href="#Footnote_490" class="fnanchor">[490]</a> or in the far ultra-violet,<a id="FNanchor_491" href="#Footnote_491" class="fnanchor">[491]</a> and the neutral nitrogen +spectrum has not as yet been arranged in series. Both sulphur and +nitrogen appear, in hotter stars, in the once and twice ionized +conditions,<a id="FNanchor_492" href="#Footnote_492" class="fnanchor">[492]</a> and are probably abundant elements in stellar +atmospheres.</p> + +<p>For the remaining elements, phosphorus, chlorine, fluorine, zirconium +and nickel, series relations are not, as yet, available. No lines of +phosphorus or the halogens have been detected in stellar spectra, but +these elements have not been satisfactorily analyzed spectroscopically, +and their apparent absence from the stars is probably a result of a +deficiency in suitable lines. Nickel and zirconium will probably be +<span class="pagenum" id="Page_187">[Pg 187]</span> +analyzed in the near future; they are both well represented in stellar +spectra, and nickel especially is probably abundant.</p> + +<p>The relative abundances, in the stellar atmosphere and the earth, +of the elements that are known to occur in both, display a striking +numerical parallelism. <a href="#TABLE_XXIX">Table XXIX</a> gives the data for the sixteen +elements most abundant in the stellar atmosphere. Successive columns +give the atomic number, the atom, the relative stellar abundance, the +relative terrestrial abundance (both for the lithosphere, hydrosphere, +and atmosphere, and for the whole earth),<a id="FNanchor_493" href="#Footnote_493" class="fnanchor">[493]</a> and the relative +abundance in stony meteorites.<a id="FNanchor_494" href="#Footnote_494" class="fnanchor">[494]</a></p> + +<h2><a id="TABLE_XXIX">TABLE XXIX</a></h2> + +<table class="autotable"> +<thead><tr> +<th class="tdc bt2 br bb" rowspan="2">Atomic number</th> +<th class="tdc bt2 br bb" rowspan="2">Atom</th> +<th class="tdc bt2 br bb" rowspan="2">Stellar Abundance</th> +<th class="tdc bt2 br bb" colspan="2">Terrestrial Abundance</th> +<th class="tdc bt2 bb" rowspan="2">Abundance<br> +Stony<br> +Meteorites</th> +</tr><tr> +<th class="tdc bt2 br bb">Crust</th> +<th class="tdc bt2 br bb">Whole Earth</th> +</tr> +</thead> +<tbody><tr> +<td class="tdc br">14</td> +<td class="tdc br">Si</td> +<td class="tdc br">5.7</td> +<td class="tdc br">16.2</td> +<td class="tdc br">9.58</td> +<td class="tdc">11.2</td> +</tr><tr> +<td class="tdc br">11</td> +<td class="tdc br">Na</td> +<td class="tdc br">5.7</td> +<td class="tdc br">2.02</td> +<td class="tdc br">0.97</td> +<td class="tdc">0.6</td> +</tr><tr> +<td class="tdc br">12</td> +<td class="tdc br">Mg</td> +<td class="tdc br">4.2</td> +<td class="tdc br">0.42</td> +<td class="tdc br">3.38</td> +<td class="tdc">2.8</td> +</tr><tr> +<td class="tdc br">13</td> +<td class="tdc br">A1</td> +<td class="tdc br">3.6</td> +<td class="tdc br">4.95</td> +<td class="tdc br">2.66</td> +<td class="tdc">1.1</td> +</tr><tr> +<td class="tdc br">6</td> +<td class="tdc br">C</td> +<td class="tdc br">3.6</td> +<td class="tdc br">0.21</td> +<td class="tdc br">....</td> +<td class="tdc">....</td> +</tr><tr> +<td class="tdc br">20</td> +<td class="tdc br">Ca</td> +<td class="tdc br">2.9</td> +<td class="tdc br">1.50</td> +<td class="tdc br">1.08</td> +<td class="tdc">0.56</td> +</tr><tr> +<td class="tdc br">26</td> +<td class="tdc br">Fe</td> +<td class="tdc br">2.5</td> +<td class="tdc br">1.48</td> +<td class="tdc br">46.37</td> +<td class="tdc">5.92</td> +</tr><tr> +<td class="tdc br">30</td> +<td class="tdc br">Zn</td> +<td class="tdc br">0.57</td> +<td class="tdc br">0.0011</td> +<td class="tdc br">....</td> +<td class="tdc">....</td> +</tr><tr> +<td class="tdc br">22</td> +<td class="tdc br">Ti</td> +<td class="tdc br">0.43</td> +<td class="tdc br">0.241</td> +<td class="tdc br">0.12</td> +<td class="tdc">....</td> +</tr><tr> +<td class="tdc br">25</td> +<td class="tdc br">Mn</td> +<td class="tdc br">0.36</td> +<td class="tdc br">0.035</td> +<td class="tdc br">0.06</td> +<td class="tdc">....</td> +</tr><tr> +<td class="tdc br">24</td> +<td class="tdc br">Cr</td> +<td class="tdc br">0.29</td> +<td class="tdc br">0.021</td> +<td class="tdc br">0.05</td> +<td class="tdc">0.29</td> +</tr><tr> +<td class="tdc br">19</td> +<td class="tdc br">K</td> +<td class="tdc br">0.11</td> +<td class="tdc br">1.088</td> +<td class="tdc br">0.38</td> +<td class="tdc">0.10</td> +</tr><tr> +<td class="tdc br">23</td> +<td class="tdc br">V</td> +<td class="tdc br">0.05</td> +<td class="tdc br">0.0133</td> +<td class="tdc br">....</td> +<td class="tdc">....</td> +</tr><tr> +<td class="tdc br">38</td> +<td class="tdc br">Sr</td> +<td class="tdc br">0.002</td> +<td class="tdc br">0.0065</td> +<td class="tdc br">....</td> +<td class="tdc">....</td> +</tr><tr> +<td class="tdc br">54</td> +<td class="tdc br">Ba</td> +<td class="tdc br">0.005</td> +<td class="tdc br">0.0098</td> +<td class="tdc br">....</td> +<td class="tdc">....</td> +</tr><tr> +<td class="tdc br bb">3</td> +<td class="tdc br bb">Li</td> +<td class="tdc br bb">0.0000</td> +<td class="tdc br bb">0.0829</td> +<td class="tdc br bb">....</td> +<td class="tdc bb">....</td> +</tr> + </tbody> +</table> + +<p>The figures in the fifth column are derived from Clarke’s estimates of +the percentage composition of the earth. The composition of the earth +has been variously estimated by different investigators, and the +<span class="pagenum" id="Page_188">[Pg 188]</span> +resulting figures depend upon theories that cannot be discussed here. +The order given by Clarke is based on the assumption of a nickel-iron +core.</p> + +<p>The numbers expressing the stellar abundance are percentages, +calculated on the assumption that the stellar and terrestrial elements +form the same fraction of the total material present. This reduces the +two columns of numbers to a form in which they are directly comparable, +but no great importance is attached to the absolute percentages in the +third column.</p> + +<p>The method that has here been used is subject to inaccuracy and +uncertainty, especially in the estimates of the exact spectral class at +which a line is first or last seen. The most that can be expected is +that the results will be trustworthy in order of magnitude. It may be +seen that the only element for which the stellar and terrestrial values +are not of the same order is zinc. Further, it appears that when the +estimates for the percentage composition of the whole earth are used +in the comparison with the stellar values, the agreement is improved +in the case of silicon, magnesium, aluminum, manganese, chromium, and +potassium; it is about the same for calcium and titanium, is less +close for sodium, and markedly poorer for iron.<a id="FNanchor_495" href="#Footnote_495" class="fnanchor">[495]</a> In the stellar +atmosphere and the meteorite the agreement is good for all the atoms +that are common to the two, but several important elements are not +recorded in the meteorite.</p> + +<p>The outstanding discrepancies between the astrophysical and terrestrial +abundances are displayed for hydrogen and helium. The enormous +abundance derived for these elements in the stellar atmosphere is +almost certainly not real. Probably the result may be considered, for +<span class="pagenum" id="Page_189">[Pg 189]</span> +hydrogen, as another aspect of its abnormal behavior, already alluded +to;<a id="FNanchor_496" href="#Footnote_496" class="fnanchor">[496]</a> and helium, which has some features of astrophysical behavior +in common with hydrogen, possibly deviates for similar reasons. The +lines of both atoms appear to be far more persistent, at high and at +low temperatures, than those of any other element.</p> + +<p>The uniformity of composition of stellar atmospheres appears to be +an established fact. The quantitative composition of the atmosphere +of a star is derived, in the present chapter, from estimates of the +“marginal appearance” of certain spectral lines, and the inferred +composition displays a striking parallel with the composition of the +earth.</p> + +<p>The observations on abundance refer merely to the stellar atmosphere, +and it is not possible to arrive in this way at conclusions as to +internal composition. But marked differences of internal composition +from star to star might be expected to affect the atmospheres to a +noticeable extent, and it is therefore somewhat unlikely that such +differences do occur.</p> + + +<div class="footnotes"><h3>FOOTNOTES:</h3> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_476" href="#FNanchor_476" class="label">[476]</a> +Russell, Science, 39, 791, 1914.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_477" href="#FNanchor_477" class="label">[477]</a> +R. H. Fowler and Milne, M. N. R. A. S., 83, 403, 1923.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_478" href="#FNanchor_478" class="label">[478]</a> +Harrison, unpub.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_479" href="#FNanchor_479" class="label">[479]</a> +H. C. 258, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_480" href="#FNanchor_480" class="label">[480]</a> +Payne, Proc. N. Ac. Sci., 11, 192, 1925.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_481" href="#FNanchor_481" class="label">[481]</a> +Clarke and Washington, Proc. N. Ac. Aci., 8, 108, 1922.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_482" href="#FNanchor_482" class="label">[482]</a> +Russell, Science, 39, 791, 1914.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_483" href="#FNanchor_483" class="label">[483]</a> +Pub. Dom. Ap. Obs., 1, 325, 1922.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_484" href="#FNanchor_484" class="label">[484]</a> +Jeffreys, The Earth, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_485" href="#FNanchor_485" class="label">[485]</a> +Shapley.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_486" href="#FNanchor_486" class="label">[486]</a> +Nature, 115, 419, 1925.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_487" href="#FNanchor_487" class="label">[487]</a> +M. N. R. A. S., 84, 665, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_488" href="#FNanchor_488" class="label">[488]</a> +Clarke and Washington, Proc. N. Ac. Sci., 8, 108, 1922.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_489" href="#FNanchor_489" class="label">[489]</a> +H. C. 256, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_490" href="#FNanchor_490" class="label">[490]</a> +Fowler, Report on Series in Line Spectra, 170, 1922.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_491" href="#FNanchor_491" class="label">[491]</a> +Hopfield, Nature, 112, 437, 1923.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_492" href="#FNanchor_492" class="label">[492]</a> +H. C. 256, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_493" href="#FNanchor_493" class="label">[493]</a> +Clarke, U. S. Geol. Surv. Prof. Pap. 132, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_494" href="#FNanchor_494" class="label">[494]</a> +G. P. Merrill, quoted by Clarke, U. S. Geol. Surv. Bul. 491.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_495" href="#FNanchor_495" class="label">[495]</a> +Professor Russell believes that iron is much more +abundant, at least in the sun, than calculated above. He writes: “More +than half of all the strong winged solar lines are iron lines, and the +strength and evident saturation of even the faint satellites in the +iron multiplets is remarkable.... There are a great many multiplets +of nearly equal strength arising from the low triplet \(F\) level in +iron.... Nothing like this happens for the \(D\) lines, or for \(H\) +and \(K\), although it may hold true for the Mg triplets. I should +consequently favor multiplying the percentage for iron by a factor +of at least 3 and probably 5—which would put it where it obviously +belongs.”</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_496" href="#FNanchor_496" class="label">[496]</a> +Chapter V, <a href="#Page_56">p. 56</a>.</p> + +</div> +</div> + + +<hr class="chap x-ebookmaker-drop"> + +<div class="chapter"> +<p><span class="pagenum" id="Page_190">[Pg 190]</span></p> + +<h2 class="nobreak" id="CHAPTER_XIV">CHAPTER XIV<br> +THE MEANING OF STELLAR CLASSIFICATION</h2> +</div> + +<p class="nind"> +IT is not necessary to discuss the possibility or desirability of +classifying stellar spectra. Both have been adequately demonstrated +by Miss Cannon in the Henry Draper Catalogue,<a id="FNanchor_497" href="#Footnote_497" class="fnanchor">[497]</a> which contains the +classification that has been accepted as standard.<a id="FNanchor_498" href="#Footnote_498" class="fnanchor">[498]</a> The catalogue +will undoubtedly long remain the authoritative source of spectral data +for the major part of the stars bright enough to be accessible to +the spectroscopist. The uses of the material that it contains are so +numerous and so direct that the basis and meaning of the classes seem +to deserve attention.</p> + +<p>In classifying a number of objects, an attempt should be made to +select criteria that will distribute the material into the most +natural groups. A classification devised with one point of view will +not necessarily appear natural from another, and the best that can +generally be done is to select the standpoint that seems to be the +most important. From all other standpoints the classification is +empirical, and must be treated as such. It seems necessary to emphasize +this empiricism with regard to the classifying of stellar spectra, +for reference is often made to the Henry Draper Classification as +though it had a theoretical, even an evolutionary, basis, whereas it +is essentially arbitrary. It is true that a classification based on +theoretical principles is very desirable, but at present there is no +adequate physical theory on which to found one.</p> + +<p>The essential feature of the Draper classification is that it aims at +classing together similar spectra, relying on general appearance, and +not on the measurement of any one line or group of lines. This has +the advantage of distributing the material in the most natural groups +possible, and a disadvantage in that different observers may find it +<span class="pagenum" id="Page_191">[Pg 191]</span> +difficult to be sure that their criteria are identically weighted.</p> + +<p>That the original aim was empirical and not theoretical is clear from +the introduction to the first extensive list of spectra classified +according to the Draper system:<a id="FNanchor_499" href="#Footnote_499" class="fnanchor">[499]</a> “It was deemed best that the +observer should place together all stars having similar spectra and +thus form an arbitrary classification rather than be hampered by any +preconceived theoretical ideas.” The present classification was the +natural outcome of such a procedure. As A. Fowler has remarked,<a id="FNanchor_500" href="#Footnote_500" class="fnanchor">[500]</a> +“the Draper classification is based essentially on the observed +spectral lines, and in reality may be regarded as independent of any +other consideration whatsoever. Even if we did not know the origin of a +single line in the stellar spectra, it is probable that we should have +arrived at precisely the same order.”</p> + +<p>The descriptions that are contained in the preface to the Henry Draper +Catalogue, and which have long been classical, were designed to +describe the salient features of the groups that had been formed. It is +only in a somewhat restricted sense that they constitute the criteria +for those groups. The descriptions were compiled from the spectra of +apparently bright stars of the classes involved, but the greater number +of the spectra actually classified are taken with such short dispersion +that all except the very strongest lines are difficult to distinguish, +and are certainly not susceptible of accurate <i>measurement</i>. This +fact should affect the standpoint of those who criticize the “multiple +nature” of the Draper criteria. A portion of one of the plates used +in the classification is herewith reproduced with no magnification. +This photograph should make it apparent to anyone familiar with the +use of spectra that the classification of stars is very largely a +<i>practical</i> problem.</p> + +<p>Instead, then, of examining the possible merits of the best theoretical +classification system, it appears to be more useful to examine the +physical implication of the most representative classification that it +has been found possible to make in practice. The fact that the Draper +<span class="pagenum" id="Page_192">[Pg 192]</span> +system is so representative has been regarded as one of its great +merits, and has rightly placed it in the authoritative position that it +occupies.</p> + +<p>When a group of stars is being studied for a special purpose, it is +often found that the Draper classes are not fine enough to subdivide +the material usefully. In such cases reclassification is often +essential. It has sometimes been suggested that this indicates that +the Draper classes are inadequate; but it must be recollected that, +for the greater part of the material contained in the Catalogue, finer +classification would have been impossible, and the subclasses in use +today represent the practical survival from a far larger number, which +were originally thought to be usable. Actually the stars represent +a continuous gradation from class to class, and in classifying it +is only possible to use the smallest distinguishable steps, which +will obviously be smaller, the larger the dispersion. When it is +found necessary to reclassify the stars more finely in a special +investigation, as in the Harvard or Mount Wilson work on spectroscopic +parallaxes,<a id="FNanchor_501" href="#Footnote_501" class="fnanchor">[501]</a> one or more measurable criteria are selected and used +as a basis, but standard stars classified at Harvard are used to define +the scale. These measured or closer classifications, while essential +for the purpose for which they were designed, have no theoretical +advantage over the Draper system (on which they are ultimately +founded), and do not, as is sometimes inferred,<a id="FNanchor_502" href="#Footnote_502" class="fnanchor">[502]</a> indicate that the +latter is in error.</p> + +<p>Although devised with no theoretical basis, the Draper classification +has long been recognized as classifying something physical, and the +fact that the majority of the stars had been ranged by it in a single +sequence suggested that a single variable was principally involved. +From general theoretical considerations it could have been predicted +that this variable was probably the temperature, but, in addition, +the observational evidence that this was the case was immediately +convincing. In the words of A. Fowler,<a id="FNanchor_503" href="#Footnote_503" class="fnanchor">[503]</a> “... the typical stars +not only increase in redness in passing through the sequence, but +successive Draper classes correspond to nearly equal increments of +redness as measured by the color index.”</p> + +<p><span class="pagenum" id="Page_193">[Pg 193]</span></p> + +<figure class="figcenter" id="i010"> +<img src="images/i010.jpg" width="800" height="1199" alt="i010"> +</figure> + +<p>The preceding eight chapters review the arguments and the observations +that have established the connection between the spectrum of a star and +its temperature. From an examination of the data there given it becomes +clear that what the Draper system classifies is essentially the degree +of thermal ionization. A. Fowler, in fact, makes the illuminating +distinctions of “arc” (\(N\) to \(G\)), “spark” (\(F\) to \(A\)), and +“superspark” (\(B\) onwards) stars.</p> + +<p>The table that follows contains, in concise form, the chief features by +which the type stars of each class are to be recognized, although it +is again emphasized that these were not actually measured as criteria +for the Draper classes. The lines characteristic of each class serve, +however, to specify its degree of thermal ionization.</p> + +<p>The homogeneity of the spectra in a given class is striking, and the +fact that large numbers of stars display exactly similar spectra +has a significance—considered in another chapter<a id="FNanchor_504" href="#Footnote_504" class="fnanchor">[504]</a>—to which +the classification problem cannot do more than call attention. The +similarity of the spectra becomes the more striking when it is +remembered that the range of conditions embraced within any one +class is very wide; the ratio in mean density may be as great as +10<a id="FNanchor_505" href="#Footnote_505" class="fnanchor">[505]</a> between stars of the same class but of differing absolute +magnitude.<a id="FNanchor_506" href="#Footnote_506" class="fnanchor">[506]</a></p> + +<p><span class="pagenum" id="Page_194">[Pg 194]</span></p> + +<p>The close spectral similarity between, giants and dwarfs, in spite of +the great differences in physical conditions, should not, however, be +misinterpreted. The observed facts are in exact accordance with what +might have been anticipated. In the first place, thermal ionization +is governed by the surface gravity, and only indirectly by the mean +density.<a id="FNanchor_507" href="#Footnote_507" class="fnanchor">[507]</a></p> + +<h2><a id="TABLE_XXX">TABLE XXX</a></h2> + +<table class="autotable"> +<thead><tr> +<th class="tdc">Class </th> +<th class="tdc_top bt2 bt2n" colspan="15">Characteristic Lines</th> +</tr> +</thead> +<tbody><tr> +<td class="tdl">O</td> +<td class="tdc">H</td> +<td class="tdc">He</td> +<td class="tdc">Si+++</td> +<td class="tdc">C++</td> +<td class="tdc">N++</td> +<td class="tdc">He+</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +</tr><tr> +<td class="tdl">\(B_0\)</td> +<td class="tdc">H</td> +<td class="tdc">He</td> +<td class="tdc">Si+++</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc">He+</td> +<td class="tdc">O+</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +</tr><tr> +<td class="tdl">\(B_1\)</td> +<td class="tdc">H</td> +<td class="tdc">He</td> +<td class="tdc">Si+++</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"> O+*</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +</tr><tr> +<td class="tdl">\(B_2\)</td> +<td class="tdc">H</td> +<td class="tdc"> He*</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +</tr><tr> +<td class="tdl">\(B_3\)</td> +<td class="tdc">H</td> +<td class="tdc">He</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +</tr><tr> +<td class="tdl">\(B_5\)</td> +<td class="tdc">H</td> +<td class="tdc">He</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc">Si+</td> +<td class="tdc">Ca+</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +</tr><tr> +<td class="tdl">\(B_8\)</td> +<td class="tdc">H</td> +<td class="tdc">He</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc">Si+</td> +<td class="tdc">Ca+</td> +<td class="tdc">Mg+</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +</tr><tr> +<td class="tdl">\(B_9\)</td> +<td class="tdc">H</td> +<td class="tdc">He</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc">Si+</td> +<td class="tdc">Ca+</td> +<td class="tdc">Mg+</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +</tr><tr> +<td class="tdl">\(A_0\)</td> +<td class="tdc"> H*</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"> Si+*</td> +<td class="tdc">Ca+</td> +<td class="tdc">Mg+</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +</tr><tr> +<td class="tdl">\(A_2\)</td> +<td class="tdc">H</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc">Ca+</td> +<td class="tdc"> Mg+*</td> +<td class="tdc">Ca</td> +<td class="tdc">Fe</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +</tr><tr> +<td class="tdl">\(A_3\)</td> +<td class="tdc">H</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc">Ca+</td> +<td class="tdc">Mg+</td> +<td class="tdc">Ca</td> +<td class="tdc">Fe</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +</tr><tr> +<td class="tdl">\(A_5\)</td> +<td class="tdc">H</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc">Ca+</td> +<td class="tdc"></td> +<td class="tdc">Ca</td> +<td class="tdc">Fe</td> +<td class="tdc">Ti</td> +<td class="tdc"></td> +<td class="tdc"></td> +</tr><tr> +<td class="tdl">\(F_0\)</td> +<td class="tdc">H</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc">Ca+</td> +<td class="tdc"></td> +<td class="tdc">Ca</td> +<td class="tdc">Fe</td> +<td class="tdc">Ti</td> +<td class="tdc"></td> +<td class="tdc"></td> +</tr><tr> +<td class="tdl_top">\(F_2\)</td> +<td class="tdc">H</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc_top">Ca+</td> +<td class="tdc"></td> +<td class="tdc_top">Ca</td> +<td class="tdc_top">Fe</td> +<td class="tdc_top">Ti</td> +<td class="tdc_top">G bd.</td> +<td class="tdc"></td> +</tr><tr> +<td class="tdl_top">\(F_5\)</td> +<td class="tdc_top">H</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc_top">Ca+</td> +<td class="tdc"></td> +<td class="tdc_top">Ca</td> +<td class="tdc_top">Fe</td> +<td class="tdc_top">Ti</td> +<td class="tdc_top">G bd.</td> +<td class="tdc"></td> +</tr><tr> +<td class="tdl_top">\(G_0\)</td> +<td class="tdc_top">H</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc_top">Ca+</td> +<td class="tdc"></td> +<td class="tdc_top">Ca</td> +<td class="tdc_top">Fe</td> +<td class="tdc_top">Ti</td> +<td class="tdc_top">G bd.</td> +<td class="tdc"></td> +</tr><tr> +<td class="tdl_top">\(K_0\)</td> +<td class="tdc_top">H</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc_top"> Ca+*</td> +<td class="tdc"></td> +<td class="tdc_top">Ca</td> +<td class="tdc_top"> Fe*</td> +<td class="tdc_top"> Ti*</td> +<td class="tdc_top"> G bd.*</td> +<td class="tdc"></td> +</tr><tr> +<td class="tdl">\(M_a\)</td> +<td class="tdc">H</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc">Ca+</td> +<td class="tdc"></td> +<td class="tdc"> Ca*</td> +<td class="tdc">Fe</td> +<td class="tdc">Ti</td> +<td class="tdc"></td> +<td class="tdc">TiO₂</td> +</tr><tr> +<td class="tdl">\(M_b\)</td> +<td class="tdc">H</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc">Ca+</td> +<td class="tdc"></td> +<td class="tdc">Ca</td> +<td class="tdc">Fe</td> +<td class="tdc">Ti</td> +<td class="tdc"></td> +<td class="tdc">TiO₂</td> +</tr><tr> +<td class="tdl">\(M_d\)</td> +<td class="tdc">H</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc">Ca+</td> +<td class="tdc"></td> +<td class="tdc">Ca</td> +<td class="tdc">Fe</td> +<td class="tdc">Ti</td> +<td class="tdc"></td> +<td class="tdc">TiO₂</td> +</tr> + </tbody> +</table> + +<p>The division into “arc,” “spark,” and “superspark” is clearly shown +by the table. Maxima of the lines which are used as criteria of class +are marked with an asterisk.</p> + +<p><span class="pagenum" id="Page_195">[Pg 195]</span></p> + +<p>It is shown in <a href="#CHAPTER_III">Chapter III</a> that the range in surface gravity is +far smaller than the range in mean density. Secondly, the basis +of the classification has been shown to be the degree of thermal +ionization.<a id="FNanchor_508" href="#Footnote_508" class="fnanchor">[508]</a> Granted that the value of the partial electron +pressure is low enough, in dwarfs as well as in giants, for thermal +ionization to predominate over ionization by collision, a mass of gas +will pass through the same <i>succession</i> of ionization-stages with +changing temperature, whatever the surface gravity. Any given stage of +ionization will, however, be reached at a lower temperature, the lower +the pressure, since, as pointed out in <a href="#CHAPTER_X">Chapter X</a>,<a id="FNanchor_509" href="#Footnote_509" class="fnanchor">[509]</a> lowered pressure +tends to increase the degree of ionization, and will help to produce a +given degree of ionization at a lower temperature.</p> + +<p>The Draper system takes no direct account of temperature. It classifies +purely by degree of ionization, and therefore, as it relates to +atmospheres in which the surface gravities differ widely, it will +produce classes that are not homogeneous in temperature; dwarfs will be +hotter than giants of the same spectral class. Fowler and Milne<a id="FNanchor_510" href="#Footnote_510" class="fnanchor">[510]</a> +anticipated a difference of from 10 to 20 per cent, and differences +in this sense and of this order actually occur.<a id="FNanchor_511" href="#Footnote_511" class="fnanchor">[511]</a> Physically it +seems to be more important to class together stars having the same +atmospheric properties than stars at exactly the same effective +temperature, although the latter might conceivably be better suited to +some purposes.</p> + +<p>Although giant and dwarf stars may be found with very similar spectra, +it is well known that they display important differences for individual +lines, and these differences have formed the basis for the estimation +of spectroscopic parallaxes.<a id="FNanchor_512" href="#Footnote_512" class="fnanchor">[512]</a> If the spectrum of a giant star is +compared with the spectrum of a dwarf of <i>the same temperature</i>, +the two will be found to differ. The line-intensities in the spectrum +of the dwarf will place it in a spectral class nearer to the red end +of the sequence—if the giant is of Class \(F_5\), the dwarf may be a +\(G_0\) star. There are two ways in which the stars might be brought +into the same spectral class; by an alteration of temperature or by +an alteration of pressure. If the temperature of the dwarf star were +<span class="pagenum" id="Page_196">[Pg 196]</span> +raised, the resulting changes in ionization in its atmosphere would +produce changes in the intensities of the lines in the spectrum. +At some temperature, about 15 per cent higher than the original +temperature of the dwarf star, it would give a spectrum resembling that +of the giant.</p> + +<figure class="figcenter" id="i011"> +<img src="images/i011.jpg" width="1600" height="1431" alt="i011"> +<figcaption class="caption"> + +<p>Figure 10</p> + +<p>Schematic representation of the ionization temperature scale for the +sequence of stellar classes. Ordinates are absolute temperatures +in thousands of degrees; abscissae are Draper classes. The points +representing the different classes have been made to lie on a straight +line, so that the temperature range of the corresponding classes shall +appear along the axis of abscissae. Vertical lines are drawn through +\(M_0\), \(K_0\), \(G_0\), \(F_0\), \(A_0\), \(B_0\), and the upper +limit of the \(O\) class, in order to show the increase in temperature +range for the hotter classes.</p></figcaption> +</figure> + +<p>If the pressure in the atmosphere of the dwarf star were reduced, the +resulting increase in the degree of ionization would also produce +changes in the spectral lines, until it gave a spectrum similar to +that of the giant. There is, however, no reason to suppose that the +<span class="pagenum" id="Page_197">[Pg 197]</span> +changes produced in the intensities of <i>individual lines</i> by these +temperature and pressure changes would be in all cases exactly equal, +although they would in general operate in the same direction.</p> + +<h2><a id="TABLE_XXXI">TABLE XXXI</a></h2> + +<table class="autotable"> +<thead><tr> +<th class="tdc bt2 bb br" rowspan="2">Class</th> +<th class="tdc bt2 bb br" rowspan="2">Effective<br> +Temperature</th> +<th class="tdc bt2 br" colspan="2">Absolute Magnitude</th> +<th class="tdc_ws2 bt2 br" colspan="2">Galactic<br> +Concentration</th> +<th class="tdc bt2 bb br" rowspan="2">Percent<br> +in<br> +H. D. C.</th> +<th class="tdc bt2 bb" rowspan="2">Space Number</th> +</tr><tr> +<th class="tdc bb">d</th> +<th class="tdc bb br">g</th> +<th class="tdc bb">7.0-8.25</th> +<th class="tdc bb br">17.0</th> +</tr> +</thead> +<tbody><tr> +<td class="tdc br">\(B_0\)</td> +<td class="tdc br">20,000°</td> +<td class="tdc"></td> +<td class="tdc br"></td> +<td class="tdc"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc"></td> +</tr><tr> +<td class="tdc br">to</td> +<td class="tdc br"></td> +<td class="tdc"></td> +<td class="tdc br">-0.50</td> +<td class="tdc"></td> +<td class="tdc br"></td> +<td class="tdc br">3.52</td> +<td class="tdc">}4.4</td> +</tr><tr> +<td class="tdc br">\(B_5\)</td> +<td class="tdc br">15,000</td> +<td class="tdc"></td> +<td class="tdc br"></td> +<td class="tdc"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc"></td> +</tr><tr> +<td class="tdc br">\(B_8\)</td> +<td class="tdc br"></td> +<td class="tdc"></td> +<td class="tdc br"></td> +<td class="tdc"></td> +<td class="tdc br">16</td> +<td class="tdc br">0.96</td> +<td class="tdc"></td> +</tr><tr> +<td class="tdc br">\(B_9\)</td> +<td class="tdc br"></td> +<td class="tdc"></td> +<td class="tdc br"></td> +<td class="tdc">50.</td> +<td class="tdc br">9.2</td> +<td class="tdc br">4.70</td> +<td class="tdc"></td> +</tr><tr> +<td class="tdc br">\(A_0\)</td> +<td class="tdc br">11,200</td> +<td class="tdc"></td> +<td class="tdc br"></td> +<td class="tdc">12.8</td> +<td class="tdc br">3.5</td> +<td class="tdc br">10.41</td> +<td class="tdc">}250</td> +</tr><tr> +<td class="tdc br">\(A_2\)</td> +<td class="tdc br"></td> +<td class="tdc"></td> +<td class="tdc br">+1.50</td> +<td class="tdc">5.3</td> +<td class="tdc br">1.8</td> +<td class="tdc br">8.89</td> +<td class="tdc"></td> +</tr><tr> +<td class="tdc br">\(A_3\)</td> +<td class="tdc br"></td> +<td class="tdc"></td> +<td class="tdc br"></td> +<td class="tdc">2.8</td> +<td class="tdc br">1.2</td> +<td class="tdc br"></td> +<td class="tdc"></td> +</tr><tr> +<td class="tdc br">\(A_5\)</td> +<td class="tdc br">8,600</td> +<td class="tdc"></td> +<td class="tdc br">+2.20</td> +<td class="tdc">1.9</td> +<td class="tdc br">1.9</td> +<td class="tdc br">2.31</td> +<td class="tdc"></td> +</tr><tr> +<td class="tdc br">\(F_0\)</td> +<td class="tdc br">7,000</td> +<td class="tdc">+2.5</td> +<td class="tdc br"></td> +<td class="tdc">1.6</td> +<td class="tdc br">1.8</td> +<td class="tdc br">5.48</td> +<td class="tdc">}680</td> +</tr><tr> +<td class="tdc br">\(F_2\)</td> +<td class="tdc br"></td> +<td class="tdc">+2.9</td> +<td class="tdc br"></td> +<td class="tdc">1.2</td> +<td class="tdc br">1.4</td> +<td class="tdc br">3.37</td> +<td class="tdc"></td> +</tr><tr> +<td class="tdc br">\(F_5\)</td> +<td class="tdc br">6,080</td> +<td class="tdc">+3.5</td> +<td class="tdc br"></td> +<td class="tdc">1.3</td> +<td class="tdc br">1.0</td> +<td class="tdc br">5.98</td> +<td class="tdc"></td> +</tr><tr> +<td class="tdc br">\(F_8\)</td> +<td class="tdc br"></td> +<td class="tdc">+4.2</td> +<td class="tdc br"></td> +<td class="tdc"></td> +<td class="tdc br"></td> +<td class="tdc br">4.28</td> +<td class="tdc">}7600</td> +</tr><tr> +<td class="tdc br">\(G_0\)</td> +<td class="tdc br">5,460</td> +<td class="tdc">+4.5</td> +<td class="tdc br">-1.5</td> +<td class="tdc"></td> +<td class="tdc br"></td> +<td class="tdc br">4.78</td> +<td class="tdc"></td> +</tr><tr> +<td class="tdc br">\(G_5\)</td> +<td class="tdc br">4,820</td> +<td class="tdc">+4.8</td> +<td class="tdc br">+0.6</td> +<td class="tdc"></td> +<td class="tdc br"></td> +<td class="tdc br">8.98</td> +<td class="tdc"></td> +</tr><tr> +<td class="tdc br">\(K_0\)</td> +<td class="tdc br">4,240</td> +<td class="tdc">+6.20</td> +<td class="tdc br">+1.05</td> +<td class="tdc"></td> +<td class="tdc br"></td> +<td class="tdc br">19.65</td> +<td class="tdc"> }160 (giant)</td> +</tr><tr> +<td class="tdc br">\(K_2\)</td> +<td class="tdc br"></td> +<td class="tdc"></td> +<td class="tdc br"></td> +<td class="tdc"></td> +<td class="tdc br"></td> +<td class="tdc br">6.85</td> +<td class="tdc"></td> +</tr><tr> +<td class="tdc br">\(K_5\)</td> +<td class="tdc br">3,600</td> +<td class="tdc">+7.20</td> +<td class="tdc br">+0.50</td> +<td class="tdc"></td> +<td class="tdc br"></td> +<td class="tdc br">4.80</td> +<td class="tdc"> }22 (giant)</td> +</tr><tr> +<td class="tdc bb br">\(M_1\)</td> +<td class="tdc bb br">3,380</td> +<td class="tdc bb">+ 10.20</td> +<td class="tdc bb br">+0.40</td> +<td class="tdc bb"></td> +<td class="tdc bb br"></td> +<td class="tdc bb br">2.10</td> +<td class="tdc bb"></td> +</tr> + </tbody> +</table> + +<p>Excitation and ionization conditions differ so widely for different +atoms that it would be expected that two factors, one of which +encourages ionization, while the other discourages recombination, would +not in every case balance exactly, even when their mean effect was +constant, as it is for any one Draper class.</p> + +<p>The Henry Draper Catalogue, as we have emphasized, was made on the +basis of the general resemblance of the spectra, an arrangement which +corresponds to the greatest physical homogeneity that can be obtained. +As regards features of their spectra, it is therefore to be expected +that the members of any one class will correspond closely, and care +<span class="pagenum" id="Page_198">[Pg 198]</span> +must be exercised in eliminating redundancies from discussions of the +homogeneity of the individual classes.</p> + +<p>There are, however, other types of discussion, independent of +spectroscopic data, and such investigations have shown that the Draper +classes have indeed a significance far beyond the mere formation +of homogeneous groups of spectra. In illustration of the profound +statistical significance of the classification, the table on <a href="#Page_197">page 197</a> +of the present chapter contains a brief synopsis of some of the +most salient features that have been correlated with spectral class. +Successive columns contain the class, the effective temperature,<a id="FNanchor_513" href="#Footnote_513" class="fnanchor">[513]</a> +the mean absolute magnitude,<a id="FNanchor_514" href="#Footnote_514" class="fnanchor">[514]</a> the galactic concentration,<a id="FNanchor_515" href="#Footnote_515" class="fnanchor">[515]</a> the +percentage of the class in the Draper catalogue,<a id="FNanchor_516" href="#Footnote_516" class="fnanchor">[516]</a> and the computed +number per million cubic parsecs.<a id="FNanchor_517" href="#Footnote_517" class="fnanchor">[517]</a></p> + + +<div class="footnotes"><h3>FOOTNOTES:</h3> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_497" href="#FNanchor_497" class="label">[497]</a> +H. A., 91-99.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_498" href="#FNanchor_498" class="label">[498]</a> +Rep. I. A. U., Rome, 1922.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_499" href="#FNanchor_499" class="label">[499]</a> +H. A., 28, 131, 1901.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_500" href="#FNanchor_500" class="label">[500]</a> +Observatory, 38, 381, 1915.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_501" href="#FNanchor_501" class="label">[501]</a> +Mt. W. Contr. 199, 1918.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_502" href="#FNanchor_502" class="label">[502]</a> +Harper and Young, J. R. A. S. Can., 18, 9, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_503" href="#FNanchor_503" class="label">[503]</a> +Observatory, 38, 381, 1915.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_504" href="#FNanchor_504" class="label">[504]</a> +Chapter XIII, <a href="#Page_178">p. 178</a>.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_505" href="#FNanchor_505" class="label">[505]</a> +Observatory, 38, 381, 1915.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_506" href="#FNanchor_506" class="label">[506]</a> +Chapter III, <a href="#Page_36">p. 36</a>.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_507" href="#FNanchor_507" class="label">[507]</a> +Chapter III, <a href="#Page_35">p. 35</a>.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_508" href="#FNanchor_508" class="label">[508]</a> +See above, <a href="#Page_193">p. 193</a>.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_509" href="#FNanchor_509" class="label">[509]</a> +<a href="#Page_141">P. 141</a>.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_510" href="#FNanchor_510" class="label">[510]</a> +M. N. R. A. S., 83, 403, 1923.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_511" href="#FNanchor_511" class="label">[511]</a> +Chapter II, <a href="#Page_31">p. 31</a>.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_512" href="#FNanchor_512" class="label">[512]</a> +Adams and Joy; Mt. W. Contr. 142, 1917.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_513" href="#FNanchor_513" class="label">[513]</a> +A. N., 219, 361, 1923.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_514" href="#FNanchor_514" class="label">[514]</a> +Lundmark, Pub. A. S. P., 34, 147, 1922.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_515" href="#FNanchor_515" class="label">[515]</a> +Shapley, H. B. 796, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_516" href="#FNanchor_516" class="label">[516]</a> +Shapley and Cannon, Proc. Am. Ac. Sci., 59, 217, 1924.</p> + +</div> + +<div class="footnote"> + +<p class="nind"><a id="Footnote_517" href="#FNanchor_517" class="label">[517]</a> +Shapley and Cannon, <i>ibid.</i>, 59, 230,1924.</p> + +</div> +</div> + + +<hr class="chap x-ebookmaker-drop"> + +<div class="chapter"> +<p><span class="pagenum" id="Page_199">[Pg 199]</span></p> + +<h2 class="nobreak" id="CHAPTER_XV">CHAPTER XV<br> +ON THE FUTURE OF THE PROBLEM</h2> +</div> + +<p class="nind"> +THE future of a subject is the product of its past, and the hopes +of astrophysics should be implicit in what the science has already +achieved. Astrophysics is a young science, however, and is still, to +some extent, in a position of choosing its route; it is very much to be +desired that present effort should so be directed that the chosen path +may lead in a permanently productive direction. The direction in which +progress lies will depend on the material available, on the development +of theory, and on the trend of thought.</p> + +<p>The material already at hand is far from exhaustively analyzed, and it +is perhaps premature to contemplate collecting more. But as a science +progresses it is often possible to direct the way “by showing the kind +of data which it is especially important to improve,” and particularly +is this the case for astrophysics. In the improvement of the old data, +by far the most important requirement is some method of standardizing +the intensities of spectrum lines, and of measuring their width, energy +distribution, and central intensity. This involves a very difficult +and necessary piece of photographic photometry. The problem is an +old one that has defied attack for a long time past. It is none the +less urgent, and until the attack has been successfully made, many +questions, such as are discussed in <a href="#CHAPTER_III">Chapter III</a>, and other questions, +which, for lack of data, we have not been able to discuss at all, must +await their precise answers.</p> + +<p>Much patient labor, on types of investigation that have already been +well worked, still remains to be done. The identification of lines in +the spectra of the sun and stars must necessarily be of a laborious +nature, but the fact that more than two thirds of the lines in +Rowland’s table are still unidentified shows how necessary and how +<span class="pagenum" id="Page_200">[Pg 200]</span> +large a piece of work this is. One of the things that would greatly +assist progress would be a revision of Rowland’s table in the light +of the recent analysis of the arc and spark spectra of the metals, +insertion of the series relations, when known, and the reduction of the +wave-length system to International Angstroms.</p> + +<p>Another line of work, which lies upon the borderland between +astrophysics and pure physics, is the analysis of spectral series. +For most of the astrophysically important lines, series relations are +already known, but some of the more difficult spectra, such as the +spectrum of nitrogen, remain unanalyzed. The analysis of all such +spectra is necessary to the advance of astrophysics.</p> + +<p>The investigation of stellar spectra has been confined, for the most +part, to the region lying between 3900 and 5000, although work on +special stars has been carried into the red and the ultra-violet. The +use of special dyes should permit work to be carried to about 7900 in +the red, and a wave-length of 3500 appears to be accessible in the +ultra-violet. There appears to be a large field for an extension of +the analysis of stellar spectra into regions of the spectrum that are +comparatively unexplored, and the writer hopes in the immediate future +to undertake work in this direction.</p> + +<p>The types of investigation hitherto mentioned are amplifications of +work already in progress. New fields are not easy to predict, but they +may be suggested by examining the extent to which present investigation +is covering the possibilities of the data. The line <i>position</i> +and <i>intensity</i> data are in full use at the present time. The +<i>form</i> and <i>energy distribution</i> of individual lines, and the +study of <i>asymmetries</i>, are among the urgent future problems. The +measurement of the <i>polarization</i> of the light received from the +stars has enormous possibilities, but so far very little success has +attended such attempts.</p> + +<p>The future progress of theory is a harder subject for prediction +than the future progress of observation. But one thing is certain: +observation must make the way for theory, and only if it does so can +the science have its greatest productivity. Observational astrophysics +<span class="pagenum" id="Page_201">[Pg 201]</span> +is so vigorous a science that the progress of theory is almost +completely determined by the progress of observation.</p> + +<p>The most important of the three factors contemplated at the opening +of the chapter is perhaps the trend of thought. It is owing to the +tendency towards laying stress on observation, and to the general +lessening of the distrust of large dimensions, that astrophysics has +become possible as a science. The surprising growth of the subject +during the last forty years is in great measure the result of this +happy chance. The growth of the subject during the next forty years +will depend on the coming trend of thought.</p> + +<p><span class="pagenum" id="Page_202">[Pg 202]</span></p> + +<p>The prospect appears encouraging. At the present time the tendency +is towards mutual toleration of point of view and to understanding +of limitations among the sciences, and a consequent increase of +correlation. If the breadth of conception thus engendered develops in +the future as it has done in the immediate past, there is hope that the +high promise of astrophysics may be brought to fruition.</p> + + +<hr class="chap x-ebookmaker-drop"> + +<div class="chapter"> +<p><span class="pagenum" id="Page_203">[Pg 203]</span></p> + +<h2 class="nobreak" id="APPENDICES">APPENDICES</h2> +</div> + +<p class="nindc space-above2"> +I. INDEX TO DEFINITIONS</p> + + +<p class="nind"> +AN attempt has been made to define specifically, at some point in the +text, most of the technical terms that are associated with the theory +of ionization. For convenience of reference, the most important of +these terms are collected into the brief index which is given below. +The references are to the pages on which the term is defined.</p> + +<table class="autotable"> +<tbody><tr> +<td class="tdl">Atomic life</td> +<td class="tdr"><a href="#Page_21">21</a>, <a href="#Page_110">110</a></td> +<td class="tdc"> </td> +<td class="tdl">Photosphere</td> +<td class="tdr"><a href="#Page_35">35</a>, <a href="#Page_47">47</a></td> +</tr><tr> +<td class="tdl">Azimuthal quantum number</td> +<td class="tdr"><a href="#Page_8">8</a>, <a href="#Page_204">204</a></td> +<td class="tdc"></td> +<td class="tdl">Quantum number</td> +<td class="tdr"><a href="#Page_8">8</a>, <a href="#Page_204">204</a></td> +</tr><tr> +<td class="tdl">Boundary temperature</td> +<td class="tdr"><a href="#Page_27">27</a></td> +<td class="tdc"></td> +<td class="tdl">Quantum relation</td> +<td class="tdr"><a href="#Page_11">11</a></td> +</tr><tr> +<td class="tdl">Displacement Rule</td> +<td class="tdr"><a href="#Page_13">13</a></td> +<td class="tdc"></td> +<td class="tdl">Residual intensity</td> +<td class="tdr"><a href="#Page_51">51</a></td> +</tr><tr> +<td class="tdl">Effective level</td> +<td class="tdr"><a href="#Page_135">135</a></td> +<td class="tdc"></td> +<td class="tdl">Reversing layer</td> +<td class="tdr"><a href="#Page_47">47</a>, <a href="#Page_49">49</a></td> +</tr><tr> +<td class="tdl">Effective temperature</td> +<td class="tdr"><a href="#Page_27">27</a></td> +<td class="tdc"></td> +<td class="tdl">Rydberg constant</td> +<td class="tdr"><a href="#Page_14">14</a>, <a href="#Page_155">155</a></td> +</tr><tr> +<td class="tdl">Excitation potential</td> +<td class="tdr"><a href="#Page_15">15</a></td> +<td class="tdc"></td> +<td class="tdl">Saturation</td> +<td class="tdr"><a href="#Page_52">52</a>, <a href="#Page_135">135</a></td> +</tr><tr> +<td class="tdl">Fractional concentration</td> +<td class="tdr"><a href="#Page_105">105</a></td> +<td class="tdc"></td> +<td class="tdl">Series notation</td> +<td class="tdr"><a href="#Page_55">55</a>, <a href="#Page_203">203</a></td> +</tr><tr> +<td class="tdl">Inner quantum number</td> +<td class="tdr"><a href="#Page_204">204</a></td> +<td class="tdc"></td> +<td class="tdr">Spectroscopic valency</td> +<td class="tdr"><a href="#Page_10">10</a></td> +</tr><tr> +<td class="tdl">Ionization potential</td> +<td class="tdr"><a href="#Page_15">15</a></td> +<td class="tdc"></td> +<td class="tdl">Subordinate lines</td> +<td class="tdr"><a href="#Page_12">12</a>, <a href="#Page_100">100</a></td> +</tr><tr> +<td class="tdl">Ionization temperature</td> +<td class="tdr"><a href="#Page_30">30</a>, <a href="#Page_132">132</a></td> +<td class="tdc"></td> +<td class="tdl">Temperature class</td> +<td class="tdr"><a href="#Page_24">24</a>, <a href="#Page_112">112</a></td> +</tr><tr> +<td class="tdl">Marginal appearance</td> +<td class="tdr"><a href="#Page_105">105</a>, <a href="#Page_135">135</a>, <a href="#Page_179">179</a></td> +<td class="tdc"></td> +<td class="tdl">Total quantum number</td> +<td class="tdr"><a href="#Page_8">8</a>, <a href="#Page_205">205</a></td> +</tr><tr> +<td class="tdl">Optical depth</td> +<td class="tdr"><a href="#Page_27">27</a>, <a href="#Page_35">35</a></td> +<td class="tdc"></td> +<td class="tdl">Ultimate lines</td> +<td class="tdr"><a href="#Page_11">11</a>, <a href="#Page_111">111</a></td> +</tr><tr> +<td class="tdl">Partial electron pressure</td> +<td class="tdr"><a href="#Page_10">10</a></td> +<td class="tdc"></td> +<td class="tdl">Valency</td> +<td class="tdr"><a href="#Page_10">10</a></td> +</tr><tr> +<td class="tdl">Partition function</td> +<td class="tdr"><a href="#Page_107">107</a></td> +<td class="tdc"></td> +<td class="tdl">Wings</td> +<td class="tdr"><a href="#Page_50">50</a>, <a href="#Page_179">179</a></td> +</tr> + </tbody> +</table> + +<p class="nindc space-above2"> +II. SERIES RELATIONS IN LINE SPECTRA</p> + + +<p class="nind"> +A SYNOPSIS of the normal series relations in line spectra has +been published by Russell and Saunders (Ap. J., 61, 39, 1925). A +transcription of the passages containing definitions of spectroscopic +quantities that are mentioned in the present volume is given below:</p> + +<p>“Every spectral line is now believed to be emitted (or absorbed) +in connection with the transition of an atom (or molecule) between +two definite (quantized) states, of different energy-content—the +frequency of the radiation being exactly proportional to the change of +energy. The wave-number of the line may therefore be expressed as the +difference of two <i>spectroscopic terms</i> which measure, in suitable +units, the energies of the initial and final states. Combinations +between these terms occur according to definite laws, which enable us +<span class="pagenum" id="Page_204">[Pg 204]</span> +to classify them into systems, each containing a number of series of +terms, which are usually multiple—</p> + +<p>“Any term \(y\) may be expressed in the form \(y = R/(m + x)^{2}\) +where \(R\) is the Rydberg constant and \(m\) an integer. For +homologous components of successive terms of the same series, \(m\) +changes by unity, while the “residual” \(x\) is sometimes practically +constant (Rydberg’s formula), or, more often, is expressible in the +form \(\mu + a/m\) (Hicks’s formula), or \(\mu + ay\) (Ritz’s formula). +In many cases this approximation fails for the smaller values of \(m\); +and prediction becomes very uncertain, though a plot of the residuals +usually gives a smooth curve....</p> + +<p>“The <i>principles of selection</i>, which determine what combinations +among these numerous terms give rise to observable lines, are very +simply expressed in terms of two sets of quantum numbers.</p> + +<p>“The <i>azimuthal quantum number</i> (\(k\)) is i for all terms of the +s-series, 2 for those of the p-series, 3 for the d’s, 4 for the f’s, 5 +for the g’s, 6 for the h’s, and so on.</p> + +<p>“Combinations usually occur only between terms of adjacent series for +which the values of \(k\) <i>differ by a unit</i>. A great many lines +are, however, known for which the change of \(k\) is 0, and a few for +which it is 2. In the simpler spectra, such lines are faint, except +when produced under the influence of a strong magnetic field; but in +the more complex spectra they are often numerous and strong.</p> + +<p>“The <i>inner quantum number</i> (\(j\)) differs from one component of +a multiple term to another, and also in the various series and systems, +according to the following scheme.</p> + +<table class="autotable"> +<thead><tr> +<th class="tdc bb bt2 br">\(k\) </th> +<th class="tdc bb bt2 br">Series</th> +<th class="tdc bb bt2 br">Singlets</th> +<th class="tdc bb bt2 br">Doublets</th> +<th class="tdc bb bt2 br">Triplets</th> +<th class="tdc bb bt2 br">Quartets</th> +<th class="tdc bb bt2 br">Quintets</th> +<th class="tdc bb bt2 br">Sextets</th> +<th class="tdc bb bt2">Septets</th> +</tr> +</thead> +<tbody><tr> +<td class="tdc br">1</td> +<td class="tdc br">s</td> +<td class="tdc br">j = 0</td> +<td class="tdc br">1</td> +<td class="tdc br">1</td> +<td class="tdc br">2</td> +<td class="tdc br">2</td> +<td class="tdc br">3</td> +<td class="tdc">3</td> +</tr><tr> +<td class="tdc br">2</td> +<td class="tdc br">p</td> +<td class="tdc br">1</td> +<td class="tdc br">1,2</td> +<td class="tdc br">0,1,2</td> +<td class="tdc br">1,2,3</td> +<td class="tdc br">1,2,3</td> +<td class="tdc br">2,3,4</td> +<td class="tdc">2,3,4</td> +</tr><tr> +<td class="tdc br">3</td> +<td class="tdc br">d</td> +<td class="tdc br">2</td> +<td class="tdc br">2,3</td> +<td class="tdc br">1,2,3</td> +<td class="tdc br">1,2,3,4</td> +<td class="tdc br">0,1,2,3,4</td> +<td class="tdc br">1,2,3,4,5</td> +<td class="tdc">1,2,3,4,5</td> +</tr><tr> +<td class="tdc br">4</td> +<td class="tdc br">f</td> +<td class="tdc br">3</td> +<td class="tdc br">3,4</td> +<td class="tdc br">2,3,4</td> +<td class="tdc br">2,3,4,5</td> +<td class="tdc br">1,2,3,4,5</td> +<td class="tdc br">1,2,3,4,5,6</td> +<td class="tdc">0,1,2,3,4,5,6</td> +</tr><tr> +<td class="tdc bb br">5</td> +<td class="tdc bb br">g</td> +<td class="tdc bb br">4</td> +<td class="tdc bb br">4,5</td> +<td class="tdc bb br">3,4,5</td> +<td class="tdc bb br">3,4,5,6</td> +<td class="tdc bb br">2,3,4,5,6</td> +<td class="tdc bb br">2,3,4,5,6,7</td> +<td class="tdc bb">1,2,3,4,5,6,7</td> +</tr> + </tbody> +</table> + +<p>“Combinations occur only between terms for which \(j\) differs by 0 or +± 1. If, however, \(j = 0\) in both cases, no radiation occurs. Lines +corresponding to a change of \(j = \pm 2\) are found in strong magnetic +fields, and a very few in their absence.</p> + +<p>“The combination of two multiple terms gives rise, therefore, to a +group of lines (which may number as many as eighteen). Such groups have +been called <i>multiplets</i> by Catalan. Their discovery has afforded +the key to the many-lined spectra....</p> + +<p>“In such a group, those lines for which the changes in \(j\) and \(k\), +in passing from one term to the other, are of the same sign, are the +strongest, and those in which they are of opposite sign the weakest. +These intensity relations are of great assistance in picking out the +multiplets.</p> + +<p>“Combinations between terms of different systems (consistent with +the foregoing rules) often occur. Such lines are usually, though not +always, faint....</p> + +<p>“The serial number \(m\) of the term (which is equivalent to the +total-quantum number) plays quite a subordinate rôle, being of +importance only when series formulae have to be calculated. An +extensive analysis of a spectrum is possible without it, though +determination of the limits of the series, and the ionization +potential, demands its introduction.”</p> + + +<p><span class="pagenum" id="Page_205">[Pg 205]</span></p> + +<h2 class="nobreak" id="APPENDIX_III">III. MATERIAL USED IN CHAPTER VIII</h2> + + +<p class="nind"> +THE line intensities quoted in <a href="#CHAPTER_VIII">Chapter VIII</a> were derived from the +spectra of the stars enumerated below in <a href="#TABLE_XXXII">Table XXXII</a>. Successive +columns contain the Draper class, the name of the star, the Boss +number, the visual apparent magnitude, and the reduced proper motion H. +The stars within each class are arranged in order of right ascension.</p> + +<h2><a id="TABLE_XXXII">TABLE XXXII</a></h2> + +<table class="autotable"> +<thead><tr> +<th class="tdc bb bt2 br"> Class </th> +<th class="tdc bb bt2 br" colspan="2"> Star </th> +<th class="tdc bb bt2 br"> Boss </th> +<th class="tdc bb bt2 br"> m </th> +<th class="tdc bb bt2 br"> H </th> +<th class="tdc bb bt2 br"> Class </th> +<th class="tdc bb bt2 br" colspan="2"> Star </th> +<th class="tdc bb bt2 br"> Boss </th> +<th class="tdc bb bt2 br"> m </th> +<th class="tdc bb bt2"> H </th> +</tr> +</thead> +<tbody><tr> +<td class="tdc br">\(B_9\)</td> +<td class="tdl">\(\lambda \)</td> +<td class="tdc br">Cen</td> +<td class="tdc br">3054</td> +<td class="tdc br">3.3</td> +<td class="tdc br">1.7</td> +<td class="tdc br">\(A_2\)</td> +<td class="tdl">\(q\)</td> +<td class="tdc br">Vel</td> +<td class="tdc br">2723</td> +<td class="tdc br">4.1</td> +<td class="tdc">5.1</td> +</tr><tr> +<td class="tdc br">\(A_0\)</td> +<td class="tdl">\(\eta\)</td> +<td class="tdc br">Phe</td> +<td class="tdc br">148</td> +<td class="tdc br">4.5</td> +<td class="tdc br">-0.5</td> +<td class="tdc br"></td> +<td class="tdl">\(\xi\)</td> +<td class="tdc br">Sgr</td> +<td class="tdc br">4832</td> +<td class="tdc br">2.7</td> +<td class="tdc">0.0</td> +</tr><tr> +<td class="tdc br"></td> +<td class="tdl">\(\nu\)</td> +<td class="tdc br">For</td> +<td class="tdc br">474</td> +<td class="tdc br">4.7</td> +<td class="tdc br">0.1</td> +<td class="tdc br"></td> +<td class="tdl">\(\epsilon\)</td> +<td class="tdc br">Gru</td> +<td class="tdc br">5880</td> +<td class="tdc br">3.7</td> +<td class="tdc">4.1</td> +</tr><tr> +<td class="tdc br"></td> +<td class="tdl">\(s\)</td> +<td class="tdc br">Eri</td> +<td class="tdc br">6ll</td> +<td class="tdc br">4.5</td> +<td class="tdc br">4.3</td> +<td class="tdc br">\(A_3\)</td> +<td class="tdl">\(\tau_3\)</td> +<td class="tdc br">Eri</td> +<td class="tdc br">696</td> +<td class="tdc br">4.2</td> +<td class="tdc">5.1</td> +</tr><tr> +<td class="tdc br"></td> +<td class="tdl">\(\alpha\)</td> +<td class="tdc br">Dor</td> +<td class="tdc br">1081</td> +<td class="tdc br">3.5</td> +<td class="tdc br">2.1</td> +<td class="tdc br"></td> +<td class="tdl">\(\beta\)</td> +<td class="tdc br">Pic</td> +<td class="tdc br">1446</td> +<td class="tdc br">3.9</td> +<td class="tdc">3.7</td> +</tr><tr> +<td class="tdc br"></td> +<td class="tdl">\(\delta\)</td> +<td class="tdc br">Vel</td> +<td class="tdc br">2356</td> +<td class="tdc br">2.0</td> +<td class="tdc br">1.9</td> +<td class="tdc br"></td> +<td class="tdl">\(\lambda\)</td> +<td class="tdc br">Mus</td> +<td class="tdc br">3092</td> +<td class="tdc br">3.8</td> +<td class="tdc">3.9</td> +</tr><tr> +<td class="tdc br"></td> +<td class="tdl">\(\beta\)</td> +<td class="tdc br">Car</td> +<td class="tdc br">2493</td> +<td class="tdc br">1.8</td> +<td class="tdc br">3.2</td> +<td class="tdc br"></td> +<td class="tdl">\(\beta\)</td> +<td class="tdc br">Pav</td> +<td class="tdc br">5315</td> +<td class="tdc br">3.6</td> +<td class="tdc">2.1</td> +</tr><tr> +<td class="tdc br"></td> +<td class="tdl">\(\gamma\)</td> +<td class="tdc br">Cen</td> +<td class="tdc br">3302</td> +<td class="tdc br">2.4</td> +<td class="tdc br">3.9</td> +<td class="tdc br"></td> +<td class="tdl">\(\alpha\)</td> +<td class="tdc br">PsA</td> +<td class="tdc br">5916</td> +<td class="tdc br">1.3</td> +<td class="tdc">4.1</td> +</tr><tr> +<td class="tdc br"></td> +<td class="tdl">\(\gamma\)</td> +<td class="tdc br">TrA</td> +<td class="tdc br">3879</td> +<td class="tdc br">3.1</td> +<td class="tdc br">2.2</td> +<td class="tdc br">\(F_0\)</td> +<td class="tdl">\(\alpha\)</td> +<td class="tdc br">Hyi</td> +<td class="tdc br">458</td> +<td class="tdc br">3.0</td> +<td class="tdc">5.0</td> +</tr><tr> +<td class="tdc br"></td> +<td class="tdl">\(\epsilon\)</td> +<td class="tdc br">Sgr</td> +<td class="tdc br">4645</td> +<td class="tdc br">2.0</td> +<td class="tdc br">2.7</td> +<td class="tdc br"></td> +<td class="tdl">\(\alpha\)</td> +<td class="tdc br">Car</td> +<td class="tdc br">1622</td> +<td class="tdc br">0.9</td> +<td class="tdc">-4.6 +<span class="pagenum" id="Page_206">[Pg 206]</span></td> +</tr><tr> +<td class="tdc br">\(F_0\)</td> +<td class="tdl">\(\iota\)</td> +<td class="tdc br">Car</td> +<td class="tdc br">2503</td> +<td class="tdc br">2.2</td> +<td class="tdc br">-0.7</td> +<td class="tdc br">\(K_0\)</td> +<td class="tdl">\(\epsilon\)</td> +<td class="tdc br">Crv</td> +<td class="tdc br">3172</td> +<td class="tdc br">3.2</td> +<td class="tdc">2.3</td> +</tr><tr> +<td class="tdc br"></td> +<td class="tdl">\(\gamma\)</td> +<td class="tdc br">Boo</td> +<td class="tdc br">3722</td> +<td class="tdc br">3.0</td> +<td class="tdc br">4.3</td> +<td class="tdc br"></td> +<td class="tdl">\(\pi^2\)</td> +<td class="tdc br">Hyi</td> +<td class="tdc br">3622</td> +<td class="tdc br">5.5</td> +<td class="tdc">4.6</td> +</tr><tr> +<td class="tdc br"></td> +<td class="tdl">\(\alpha\)</td> +<td class="tdc br">Cir</td> +<td class="tdc br">3739</td> +<td class="tdc br">3.4</td> +<td class="tdc br">5.0</td> +<td class="tdc br"></td> +<td class="tdl">\(\theta\)</td> +<td class="tdc br">Cen</td> +<td class="tdc br">3623</td> +<td class="tdc br">2.3</td> +<td class="tdc">6.7</td> +</tr><tr> +<td class="tdc br"></td> +<td class="tdl">\(\beta\)</td> +<td class="tdc br">TrA</td> +<td class="tdc br">4030</td> +<td class="tdc br">3.0</td> +<td class="tdc br">6.2</td> +<td class="tdc br"></td> +<td class="tdl">\(\zeta\)</td> +<td class="tdc br">Lup</td> +<td class="tdc br">3864</td> +<td class="tdc br">3.5</td> +<td class="tdc">4.0</td> +</tr><tr> +<td class="tdc br"></td> +<td class="tdl">\(\theta\)</td> +<td class="tdc br">Sco</td> +<td class="tdc br">4457</td> +<td class="tdc br">2.0</td> +<td class="tdc br">-2.6</td> +<td class="tdc br"></td> +<td class="tdl">\(\nu\)</td> +<td class="tdc br">Lib</td> +<td class="tdc br">3962</td> +<td class="tdc br">5.3</td> +<td class="tdc">-1.2</td> +</tr><tr> +<td class="tdc br">\(F_2\)</td> +<td class="tdl">\(\eta\)</td> +<td class="tdc br">Sco</td> +<td class="tdc br">4361</td> +<td class="tdc br">3.4</td> +<td class="tdc br">5.7</td> +<td class="tdc br"></td> +<td class="tdl">\(\gamma\)</td> +<td class="tdc br">Apo</td> +<td class="tdc br">4168</td> +<td class="tdc br">3.9</td> +<td class="tdc">4.6</td> +</tr><tr> +<td class="tdc br"></td> +<td class="tdl">\(\pi\)</td> +<td class="tdc br">Sgr</td> +<td class="tdc br">4874</td> +<td class="tdc br">3.0</td> +<td class="tdc br">1.0</td> +<td class="tdc br"></td> +<td class="tdl">\(\epsilon\)</td> +<td class="tdc br">Sco</td> +<td class="tdc br">4272</td> +<td class="tdc br">2.4</td> +<td class="tdc">6.5</td> +</tr><tr> +<td class="tdc br">\(F_5\)</td> +<td class="tdl">\(\delta\)</td> +<td class="tdc br">Vol</td> +<td class="tdc br">1917</td> +<td class="tdc br">4.0</td> +<td class="tdc br">0.6</td> +<td class="tdc br"></td> +<td class="tdl">\(\gamma\)</td> +<td class="tdc br">Sgr</td> +<td class="tdc br">4568</td> +<td class="tdc br">3.1</td> +<td class="tdc">4.6</td> +</tr><tr> +<td class="tdc br"></td> +<td class="tdl">\(\alpha\)</td> +<td class="tdc br">CMi</td> +<td class="tdc br">2008</td> +<td class="tdc br">0.5</td> +<td class="tdc br">6.1</td> +<td class="tdc br"></td> +<td class="tdl">\(\delta\)</td> +<td class="tdc br">Sgr</td> +<td class="tdc br">4628</td> +<td class="tdc br">2.8</td> +<td class="tdc">1.3</td> +</tr><tr> +<td class="tdc br"></td> +<td class="tdl">\(\rho\)</td> +<td class="tdc br">Pup</td> +<td class="tdc br">2153</td> +<td class="tdc br">2.9</td> +<td class="tdc br">2.9</td> +<td class="tdc br"></td> +<td class="tdl">\(\lambda\)</td> +<td class="tdc br">Sgr</td> +<td class="tdc br">4665</td> +<td class="tdc br">2.9</td> +<td class="tdc">4.4</td> +</tr><tr> +<td class="tdc br"></td> +<td class="tdl">\(b\)</td> +<td class="tdc br">Vel</td> +<td class="tdc br">2324</td> +<td class="tdc br">4.1</td> +<td class="tdc br">0.0</td> +<td class="tdc br"></td> +<td class="tdl">\(\xi^2\)</td> +<td class="tdc br">Sgr</td> +<td class="tdc br">4809</td> +<td class="tdc br">3.6</td> +<td class="tdc">1.4</td> +</tr><tr> +<td class="tdc br"></td> +<td class="tdl">\(d\)</td> +<td class="tdc br">Oph</td> +<td class="tdc br">4421</td> +<td class="tdc br">4.4</td> +<td class="tdc br">5.4</td> +<td class="tdc br"></td> +<td class="tdl">\(\tau\)</td> +<td class="tdc br">Sgr</td> +<td class="tdc br">4857</td> +<td class="tdc br">3.4</td> +<td class="tdc">5.5</td> +</tr><tr> +<td class="tdc br"></td> +<td class="tdl">\(\iota_1\)</td> +<td class="tdc br">Sco</td> +<td class="tdc br">4492</td> +<td class="tdc br">3.1</td> +<td class="tdc br">-3.9</td> +<td class="tdc br"></td> +<td class="tdl">\(\alpha\)</td> +<td class="tdc br">Ind</td> +<td class="tdc br">5281</td> +<td class="tdc br">3.2</td> +<td class="tdc">2.5</td> +</tr><tr> +<td class="tdc br"></td> +<td class="tdl">\(\kappa\)</td> +<td class="tdc br">Pav</td> +<td class="tdc br">4778</td> +<td class="tdc br">var.</td> +<td class="tdc br">0.0</td> +<td class="tdc br"></td> +<td class="tdl">\(c_2\)</td> +<td class="tdc br">Aqr</td> +<td class="tdc br">5963</td> +<td class="tdc br">3.8</td> +<td class="tdc">0.5</td> +</tr><tr> +<td class="tdc br">\(F_8\)</td> +<td class="tdl">\(\zeta\)</td> +<td class="tdc br">Tuc</td> +<td class="tdc br">55</td> +<td class="tdc br">4.3</td> +<td class="tdc br">10.9</td> +<td class="tdc br"></td> +<td class="tdl">\(\iota\)</td> +<td class="tdc br">Gru</td> +<td class="tdc br">5965</td> +<td class="tdc br">4.1</td> +<td class="tdc">4.9</td> +</tr><tr> +<td class="tdc br"></td> +<td class="tdl">\(\alpha\)</td> +<td class="tdc br">For</td> +<td class="tdc br">723</td> +<td class="tdc br">4.0</td> +<td class="tdc br">8.3</td> +<td class="tdc br">\(K_2\)</td> +<td class="tdl">\(\epsilon\)</td> +<td class="tdc br">Cru</td> +<td class="tdc br">3218</td> +<td class="tdc br">3.6</td> +<td class="tdc">5.1</td> +</tr><tr> +<td class="tdc br"></td> +<td class="tdl">\(\gamma\)</td> +<td class="tdc br">Lep</td> +<td class="tdc br">1420</td> +<td class="tdc br">3.8</td> +<td class="tdc br">9.7,7.1</td> +<td class="tdc br"></td> +<td class="tdl">\(\delta\)</td> +<td class="tdc br">Mus</td> +<td class="tdc br">3377</td> +<td class="tdc br">3.6</td> +<td class="tdc">5.7</td> +</tr><tr> +<td class="tdc br"></td> +<td class="tdl">\(\delta\)</td> +<td class="tdc br">CMa</td> +<td class="tdc br">1839</td> +<td class="tdc br">2.0</td> +<td class="tdc br">-4.5</td> +<td class="tdc br"></td> +<td class="tdl">\(\alpha\)</td> +<td class="tdc br">TrA</td> +<td class="tdc br">4250</td> +<td class="tdc br">1.9</td> +<td class="tdc">-0.6</td> +</tr><tr> +<td class="tdc br">\(G_0\)</td> +<td class="tdl">\(\beta\)</td> +<td class="tdc br">Hyi</td> +<td class="tdc br">74</td> +<td class="tdc br">2.9</td> +<td class="tdc br">9.7</td> +<td class="tdc br"></td> +<td class="tdl">\(\beta\)</td> +<td class="tdc br">Ara</td> +<td class="tdc br">4406</td> +<td class="tdc br">2.8</td> +<td class="tdc">0.6</td> +</tr><tr> +<td class="tdc br"></td> +<td class="tdl">\(\alpha\)</td> +<td class="tdc br">Aur</td> +<td class="tdc br">1246</td> +<td class="tdc br">0.2</td> +<td class="tdc br">3.4</td> +<td class="tdc br"></td> +<td class="tdl">\(\alpha\)</td> +<td class="tdc br">Tuc</td> +<td class="tdc br">5747</td> +<td class="tdc br">2.9</td> +<td class="tdc">2.6</td> +</tr><tr> +<td class="tdc br"></td> +<td class="tdl">\(\beta\)</td> +<td class="tdc br">Lep</td> +<td class="tdc br">1323</td> +<td class="tdc br">3.0</td> +<td class="tdc br">2.9</td> +<td class="tdc br">\(K_5\)</td> +<td class="tdl">\(\alpha\)</td> +<td class="tdc br">Tau</td> +<td class="tdc br">1077</td> +<td class="tdc br">1.1</td> +<td class="tdc">2.6</td> +</tr><tr> +<td class="tdc br"></td> +<td class="tdl">\(\xi\)</td> +<td class="tdc br">Pup</td> +<td class="tdc br">2065</td> +<td class="tdc br">3.5</td> +<td class="tdc br">-2.3</td> +<td class="tdc br"></td> +<td class="tdl">\(\pi\)</td> +<td class="tdc br">Pup</td> +<td class="tdc br">1896</td> +<td class="tdc br">2.7</td> +<td class="tdc">-2.8</td> +</tr><tr> +<td class="tdc br"></td> +<td class="tdl">\(\epsilon\)</td> +<td class="tdc br">Leo</td> +<td class="tdc br">2618</td> +<td class="tdc br">3.1</td> +<td class="tdc br">1.5</td> +<td class="tdc br"></td> +<td class="tdl">\(\delta\)</td> +<td class="tdc br">Pup</td> +<td class="tdc br">1972</td> +<td class="tdc br">3.3</td> +<td class="tdc">4.7</td> +</tr><tr> +<td class="tdc br"></td> +<td class="tdl">\(l\)</td> +<td class="tdc br">Car</td> +<td class="tdc br">2628</td> +<td class="tdc br">var.</td> +<td class="tdc br">1.1</td> +<td class="tdc br"></td> +<td class="tdl">\(q\)</td> +<td class="tdc br">Car</td> +<td class="tdc br">2739</td> +<td class="tdc br">3.4</td> +<td class="tdc">1.7</td> +</tr><tr> +<td class="tdc br"></td> +<td class="tdl">\(\zeta\)</td> +<td class="tdc br">Cap</td> +<td class="tdc br">5507</td> +<td class="tdc br">3.9</td> +<td class="tdc br">(1.1)</td> +<td class="tdc br"></td> +<td class="tdl">\(\alpha\)</td> +<td class="tdc br">Apo</td> +<td class="tdc br">3746</td> +<td class="tdc br">3.8</td> +<td class="tdc">1.4</td> +</tr><tr> +<td class="tdc br">\(G_5\)</td> +<td class="tdl">\(\alpha\)</td> +<td class="tdc br">Ret</td> +<td class="tdc br">994</td> +<td class="tdc br">3.4</td> +<td class="tdc br">2.6</td> +<td class="tdc br"></td> +<td class="tdl">\(\eta\)</td> +<td class="tdc br">Ara</td> +<td class="tdc br">4265</td> +<td class="tdc br">3.7</td> +<td class="tdc">2.5</td> +</tr><tr> +<td class="tdc br"></td> +<td class="tdl">\(\mu\)</td> +<td class="tdc br">Vel</td> +<td class="tdc br">2875</td> +<td class="tdc br">2.8</td> +<td class="tdc br">2.3</td> +<td class="tdc br"></td> +<td class="tdl">\(\zeta^2\)</td> +<td class="tdc br">Sco</td> +<td class="tdc br">4292</td> +<td class="tdc br">3.8</td> +<td class="tdc">5.9</td> +</tr><tr> +<td class="tdc br"></td> +<td class="tdl">\(\xi\)</td> +<td class="tdc br">Hya</td> +<td class="tdc br">3042</td> +<td class="tdc br">3.7</td> +<td class="tdc br">5.3</td> +<td class="tdc br"></td> +<td class="tdl">\(\zeta\)</td> +<td class="tdc br">Ara</td> +<td class="tdc br">4304</td> +<td class="tdc br">3.1</td> +<td class="tdc">1.5</td> +</tr><tr> +<td class="tdc br"></td> +<td class="tdl">\(\beta\)</td> +<td class="tdc br">Crv</td> +<td class="tdc br">3280</td> +<td class="tdc br">2.8</td> +<td class="tdc br">1.7</td> +<td class="tdc br">\(M_a\)</td> +<td class="tdl">\(\beta\)</td> +<td class="tdc br">And</td> +<td class="tdc br">259</td> +<td class="tdc br">2.4</td> +<td class="tdc">-0.8</td> +</tr><tr> +<td class="tdc br"></td> +<td class="tdl">\(\gamma\)</td> +<td class="tdc br">Hya</td> +<td class="tdc br">3449</td> +<td class="tdc br">3.3</td> +<td class="tdc br">2.9</td> +<td class="tdc br"></td> +<td class="tdl">\(\gamma\)</td> +<td class="tdc br">Hyi</td> +<td class="tdc br">899</td> +<td class="tdc br">3.2</td> +<td class="tdc">-1.3</td> +</tr><tr> +<td class="tdc br"></td> +<td class="tdl">\(\beta\)</td> +<td class="tdc br">CrA</td> +<td class="tdc br">4871</td> +<td class="tdc br">4.2</td> +<td class="tdc br">2.0</td> +<td class="tdc br"></td> +<td class="tdl">\(\alpha\)</td> +<td class="tdc br">Ori</td> +<td class="tdc br">1468</td> +<td class="tdc br">0.9</td> +<td class="tdc">-0.0</td> +</tr><tr> +<td class="tdc br"></td> +<td class="tdl">\(\delta\)</td> +<td class="tdc br">Pav</td> +<td class="tdc br">5138</td> +<td class="tdc br">3.6</td> +<td class="tdc br">9.7</td> +<td class="tdc br"></td> +<td class="tdl">\(\alpha\)</td> +<td class="tdc br">Sco</td> +<td class="tdc br">4193</td> +<td class="tdc br">1.2</td> +<td class="tdc">-2.5</td> +</tr><tr> +<td class="tdc br">\(K_0\)</td> +<td class="tdl">\(\alpha\)</td> +<td class="tdc br">Phe</td> +<td class="tdc br">78</td> +<td class="tdc br">2.4</td> +<td class="tdc br">5.6</td> +<td class="tdc br">\(M_b\)</td> +<td class="tdl">\(\tau_4\)</td> +<td class="tdc br">Eri</td> +<td class="tdc br">759</td> +<td class="tdc br">4.0</td> +<td class="tdc">3.2</td> +</tr><tr> +<td class="tdc br"></td> +<td class="tdl">\(\alpha\)</td> +<td class="tdc br">Cas</td> +<td class="tdc br">135</td> +<td class="tdc br">2.5</td> +<td class="tdc br">1.4</td> +<td class="tdc br"></td> +<td class="tdl">\(\gamma\)</td> +<td class="tdc br">Cru</td> +<td class="tdc br">3263</td> +<td class="tdc br">1.6</td> +<td class="tdc">3.8</td> +</tr><tr> +<td class="tdc br"></td> +<td class="tdl">\(\beta\)</td> +<td class="tdc br">Phe</td> +<td class="tdc br">245</td> +<td class="tdc br">3.4</td> +<td class="tdc br">1.6</td> +<td class="tdc br"></td> +<td class="tdl">\(\gamma\)</td> +<td class="tdc br">Lib</td> +<td class="tdc br">3837</td> +<td class="tdc br">3.4</td> +<td class="tdc">3.3</td> +</tr><tr> +<td class="tdc br"></td> +<td class="tdl">\(\delta\)</td> +<td class="tdc br">Phe</td> +<td class="tdc br">336</td> +<td class="tdc br">4.0</td> +<td class="tdc br">5.4</td> +<td class="tdc br"></td> +<td class="tdl">\(\alpha\)</td> +<td class="tdc br">Her</td> +<td class="tdc br">4373</td> +<td class="tdc br">3.5</td> +<td class="tdc">0.9</td> +</tr><tr> +<td class="tdc br"></td> +<td class="tdl">\(\beta\)</td> +<td class="tdc br">Ret</td> +<td class="tdc br">875</td> +<td class="tdc br">3.8</td> +<td class="tdc br">6.2</td> +<td class="tdc br"></td> +<td class="tdl">\(\eta\)</td> +<td class="tdc br">Sgr</td> +<td class="tdc br">4617</td> +<td class="tdc br">3.2</td> +<td class="tdc">4.9</td> +</tr><tr> +<td class="tdc br"></td> +<td class="tdl">\(\delta\)</td> +<td class="tdc br">Lep</td> +<td class="tdc br">1456</td> +<td class="tdc br">39</td> +<td class="tdc br">8.1</td> +<td class="tdc br"></td> +<td class="tdl">\(\beta\)</td> +<td class="tdc br">Gru</td> +<td class="tdc br">5854</td> +<td class="tdc br">2.2</td> +<td class="tdc">2.8</td> +</tr><tr> +<td class="tdc bb br"></td> +<td class="tdl bb">\(\beta\)</td> +<td class="tdc bb br">Col</td> +<td class="tdc bb br">1459</td> +<td class="tdc bb br">3.2</td> +<td class="tdc bb br">6.2</td> +<td class="tdc bb br"></td> +<td class="tdc bb"></td> +<td class="tdc bb br"></td> +<td class="tdc bb br"></td> +<td class="tdc bb br"></td> +<td class="tdc bb"></td> +</tr> + </tbody> +</table> + +<p><span class="pagenum" id="Page_207">[Pg 207]</span></p> + +<p class="nindc space-above2"> +IV. INTENSITY CHANGES OF LINES WITH UNKNOWN +SERIES RELATIONS</p> + + +<p class="nind"> +THE following tabulation shows the intensity changes of lines +of unknown series relations that occur in the hotter stars. The +arrangement follows that of <a href="#TABLE_XIX">Table XIX</a>. Notes on the maxima and blends +are appended.</p> + +<h2><a id="TABLE_XXXIII">TABLE XXXIII</a></h2> + +<table class="autotable"> +<thead><tr> +<th class="tdc bb bt2 br"> Atom </th> +<th class="tdc bb bt2 br"> Line </th> +<th class="tdc bb bt2">\(\zeta\) Pup</th> +<th class="tdc bb bt2">\(\tau CM_a\)</th> +<th class="tdc bb bt2">\(_{29}CM_a\)</th> +<th class="tdc bb bt2">\(B_0\)</th> +<th class="tdc bb bt2">\(B_0\)</th> +<th class="tdc bb bt2">\(B_1\)</th> +<th class="tdc bb bt2">\(B_2\)</th> +<th class="tdc bb bt2">\(B_3\)</th> +<th class="tdc bb bt2">\(B_5\)</th> +<th class="tdc bb bt2">\(B_8\)</th> +<th class="tdc bb bt2">\(B_9\)</th> +<th class="tdc bb bt2">\(A_0\)</th> +<th class="tdc bb bt2 br">\(A_2\)</th> +<th class="tdc bb bt2">Note</th> +</tr> +</thead> +<tbody><tr> +<td class="tdc br">C++</td> +<td class="tdl br">4649</td> +<td class="tdc">0.0</td> +<td class="tdc">2.0</td> +<td class="tdc">9.0</td> +<td class="tdc">6.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc br">..</td> +<td class="tdc">1</td> +</tr><tr> +<td class="tdc br">N+</td> +<td class="tdl br">3996.9</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">5.0</td> +<td class="tdc">6.0</td> +<td class="tdc">7.0</td> +<td class="tdc">..</td> +<td class="tdc">9.0</td> +<td class="tdc">..</td> +<td class="tdc">..</td> +<td class="tdc">5.0</td> +<td class="tdc br">0.0</td> +<td class="tdc">1</td> +</tr><tr> +<td class="tdc br">N++</td> +<td class="tdl br">4515.0</td> +<td class="tdc">..</td> +<td class="tdc">9.0</td> +<td class="tdc">4.0</td> +<td class="tdc">4.0</td> +<td class="tdc">1.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc br">0.0</td> +<td class="tdc">2</td> +</tr><tr> +<td class="tdc br"></td> +<td class="tdl br">4097.5</td> +<td class="tdc">..</td> +<td class="tdc">15.0</td> +<td class="tdc">8.0</td> +<td class="tdc">5.0</td> +<td class="tdc">..</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc br">0.0</td> +<td class="tdc">3</td> +</tr><tr> +<td class="tdc br">O+</td> +<td class="tdl br">4943.4</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">4.0</td> +<td class="tdc">4.0</td> +<td class="tdc">3.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc br">0.0</td> +<td class="tdc">1</td> +</tr><tr> +<td class="tdc br"></td> +<td class="tdl br">4941.2</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc br"></td> +<td class="tdc"></td> +</tr><tr> +<td class="tdc br"></td> +<td class="tdl br">4705.3</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">2.0</td> +<td class="tdc">4.0</td> +<td class="tdc">4.0</td> +<td class="tdc">3.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc br">0.0</td> +<td class="tdc">2</td> +</tr><tr> +<td class="tdc br"></td> +<td class="tdl br">4699.2</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc br"></td> +<td class="tdc"></td> +</tr><tr> +<td class="tdc br"></td> +<td class="tdl br">4676.2</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">2.0</td> +<td class="tdc">5.0</td> +<td class="tdc">..</td> +<td class="tdc">7.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc br">0.0</td> +<td class="tdc">3</td> +</tr><tr> +<td class="tdc br"></td> +<td class="tdl br">4661.6</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">2.0</td> +<td class="tdc">5.0</td> +<td class="tdc">..</td> +<td class="tdc">7.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc br">0.0</td> +<td class="tdc">4</td> +</tr><tr> +<td class="tdc br"></td> +<td class="tdl br">4649.1</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">6.0</td> +<td class="tdc">9.0</td> +<td class="tdc">12.0</td> +<td class="tdc">9.0</td> +<td class="tdc">..</td> +<td class="tdc">4.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc br">0.0</td> +<td class="tdc">5</td> +</tr><tr> +<td class="tdc br"></td> +<td class="tdl br">4641.8</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">3.0</td> +<td class="tdc">10.0</td> +<td class="tdc">7.0</td> +<td class="tdc">..</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc br">0.0</td> +<td class="tdc">6</td> +</tr><tr> +<td class="tdc br"></td> +<td class="tdl br">4596.2</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">1.0</td> +<td class="tdc">5.0</td> +<td class="tdc">..</td> +<td class="tdc">6.0</td> +<td class="tdc">..</td> +<td class="tdc">3.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc br">0.0</td> +<td class="tdc">7</td> +</tr><tr> +<td class="tdc br"></td> +<td class="tdl br">4591.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">1.0</td> +<td class="tdc">5.0</td> +<td class="tdc">..</td> +<td class="tdc">6.0</td> +<td class="tdc">..</td> +<td class="tdc">3.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc br">0.0</td> +<td class="tdc">8</td> +</tr><tr> +<td class="tdc br"></td> +<td class="tdl br">4417.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">5.0</td> +<td class="tdc">6.0</td> +<td class="tdc">11.0</td> +<td class="tdc">3.0</td> +<td class="tdc">..</td> +<td class="tdc">2.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc br">0.0</td> +<td class="tdc">9</td> +</tr><tr> +<td class="tdc br"></td> +<td class="tdl br">4415.9</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc"></td> +<td class="tdc">3.0</td> +<td class="tdc">..</td> +<td class="tdc">2.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc br">0.0</td> +<td class="tdc">10</td> +</tr><tr> +<td class="tdc br"></td> +<td class="tdl br">4366.9</td> +<td class="tdc">0.0</td> +<td class="tdc">4.0</td> +<td class="tdc">4.0</td> +<td class="tdc">4.0</td> +<td class="tdc">..</td> +<td class="tdc">6.0</td> +<td class="tdc">6.0</td> +<td class="tdc">..</td> +<td class="tdc">1.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc br">0.0</td> +<td class="tdc">11</td> +</tr><tr> +<td class="tdc br"></td> +<td class="tdl br">4075.9</td> +<td class="tdc">0.0</td> +<td class="tdc">3.0</td> +<td class="tdc">0.0</td> +<td class="tdc">2.0</td> +<td class="tdc">6.0</td> +<td class="tdc">8.0</td> +<td class="tdc">6.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc br">0.0</td> +<td class="tdc">12</td> +</tr><tr> +<td class="tdc br"></td> +<td class="tdl br">4072.2</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">2.0</td> +<td class="tdc">7.0</td> +<td class="tdc">9.0</td> +<td class="tdc">6.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc br">0.0</td> +<td class="tdc">13</td> +</tr><tr> +<td class="tdc br"></td> +<td class="tdl br">4069.9</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">4.0</td> +<td class="tdc">6.0</td> +<td class="tdc">8.0</td> +<td class="tdc">6.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc br">0.0</td> +<td class="tdc">14</td> +</tr><tr> +<td class="tdc br">S+</td> +<td class="tdl br">4815</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">x</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc br">0.0</td> +<td class="tdc">1</td> +</tr><tr> +<td class="tdc br"></td> +<td class="tdl br">4174.5</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">3.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc br">0.0</td> +<td class="tdc">2</td> +</tr><tr> +<td class="tdc br"></td> +<td class="tdl br">4162.9</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">3.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc br">0.0</td> +<td class="tdc">3</td> +</tr><tr> +<td class="tdc br">S++</td> +<td class="tdl br">4295</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">1.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc br">0.0</td> +<td class="tdc">4</td> +</tr><tr> +<td class="tdc br"></td> +<td class="tdl br">4285.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">6.0</td> +<td class="tdc">4.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc">0.0</td> +<td class="tdc br">0.0</td> +<td class="tdc">5</td> +</tr><tr> +<td class="tdc bb br"></td> +<td class="tdl bb br">4253.8</td> +<td class="tdc bb">0.0</td> +<td class="tdc bb">0.0</td> +<td class="tdc bb">0.0</td> +<td class="tdc bb">0.0</td> +<td class="tdc bb">6.2</td> +<td class="tdc bb">6.8</td> +<td class="tdc bb">6.0</td> +<td class="tdc bb">0.0</td> +<td class="tdc bb">0.0</td> +<td class="tdc bb">0.0</td> +<td class="tdc bb">0.0</td> +<td class="tdc bb">0.0</td> +<td class="tdc bb br">0.0</td> +<td class="tdc bb">6</td> +</tr> + </tbody> +</table> +<p class="nindc" > +NOTES TO TABLE XXXIII</p> +<table class="autotable"> +<thead><tr> +<th class="tdc">Atom </th> +<th class="tdc">Note </th> +<th class="tdl">Maximum </th> +<th class="tdc">Remarks</th> +</tr> +</thead> +<tbody><tr> +<td class="tdl_top">C++</td> +<td class="tdc_top"><a id="1r">1</a></td> +<td class="tdl_top">\(_{29}CM_a\)</td> +<td class="tdl_bot">Line blended, in stars cooler than \(B_0\), with V+ 4649.1. +Attributed by Fowler and Milne, and by Hartree, to C+++</td> +</tr><tr> +<td class="tdl_top">N+</td> +<td class="tdc_top"><a id="1s">1</a></td> +<td class="tdl_top">\(B_5\)</td> +<td class="tdl_top">Unblended</td> +</tr><tr> +<td class="tdl_top">N++</td> +<td class="tdc_top"><a id="2s">2</a></td> +<td class="tdl_top">\(\tau CM_a\)</td> +<td class="tdl_top"></td> +</tr><tr> +<td class="tdl_top"></td> +<td class="tdc_top"><a id="3s">3</a></td> +<td class="tdl_top">\(\tau CM_a\)</td> +<td class="tdl_top">Blended with the Si+++ line at 4096, which is probably +effective throughout the whole range</td> +</tr><tr> +<td class="tdl_top">O+</td> +<td class="tdc_top"><a id="1t">1</a></td> +<td class="tdl_top">\(B_0-B_1\)</td> +<td class="tdl_top"></td> +</tr><tr> +<td class="tdl_top"></td> +<td class="tdc_top"><a id="2t">2</a></td> +<td class="tdl_top">\(B_0-B_1\)</td> +<td class="tdl_top"></td> +</tr><tr> +<td class="tdl_top"></td> +<td class="tdc_top"><a id="3t">3</a></td> +<td class="tdl_top">\(B_2\)?</td> +<td class="tdl_top"></td> +</tr><tr> +<td class="tdl_top"></td> +<td class="tdc_top"><a id="4t">4</a></td> +<td class="tdl_top">\(B_2\)?</td> +<td class="tdl_top"></td> +</tr><tr> +<td class="tdl_top"></td> +<td class="tdc_top"><a id="5t">5</a></td> +<td class="tdl_top">\(B_1\)</td> +<td class="tdl_top">Blended with C++ line at 4649, which preponderates +in stars hotter than \(B_0\), and probably contributes +largely in that class</td> +</tr><tr> +<td class="tdl_top"></td> +<td class="tdc_top"><a id="6t">6</a></td> +<td class="tdl_top">\(B_1\)</td> +<td class="tdl_top"></td> +</tr><tr> +<td class="tdl_top"></td> +<td class="tdc_top"><a id="7t">7</a></td> +<td class="tdl_top">\(B_2\)</td> +<td class="tdl_top"></td> +</tr><tr> +<td class="tdl_top"></td> +<td class="tdc_top"><a id="8t">8</a></td> +<td class="tdl_top">\(B_2\)</td> +<td class="tdl_top"></td> +</tr><tr> +<td class="tdl_top"></td> +<td class="tdc_top"><a id="9t">9</a></td> +<td class="tdl_top">\(B_1\)</td> +<td class="tdl_top"></td> +</tr><tr> +<td class="tdl_top"></td> +<td class="tdc_top"><a id="10t">10</a></td> +<td class="tdl_top">\(B_1\)</td> +<td class="tdl_top"></td> +</tr><tr> +<td class="tdl_top"></td> +<td class="tdc_top"><a id="11t">11</a></td> +<td class="tdl_top">\(B_1-B_2\)?</td> +<td class="tdl_top">Certainly another line is here involved, but it has not +been identified</td> +</tr><tr> +<td class="tdl_top"></td> +<td class="tdc_top"><a id="12t">12</a></td> +<td class="tdl_top">\(B_1\)</td> +<td class="tdl_top"></td> +</tr><tr> +<td class="tdl_top"></td> +<td class="tdc_top"><a id="13t">13</a></td> +<td class="tdl_top">\(B_1\)</td> +<td class="tdl_top"></td> +</tr><tr> +<td class="tdl_top"></td> +<td class="tdc_top"><a id="14t">14</a></td> +<td class="tdl_top">\(B_1\)</td> +<td class="tdl_top"></td> +</tr><tr> +<td class="tdl_top">S+</td> +<td class="tdc_top"><a id="1u">1</a> <a id="2u">2</a> <a id="3u">3</a></td> +<td class="tdl_top">\(B_8\)</td> +<td class="tdl_top">Lines recorded by Lockyer; not measured by the writer</td> +</tr><tr> +<td class="tdl_top">S++</td> +<td class="tdc_top"><a id="4u">4</a></td> +<td class="tdl_top">\(B_1\)</td> +<td class="tdl_top">Line recorded by Lockyer. Intensity from H.A., 28; +not measured by the writer</td> +</tr><tr> +<td class="tdl_top"></td> +<td class="tdc_top"><a id="5u">5</a></td> +<td class="tdl_top">\(B_1\)</td> +<td class="tdl_top"></td> +</tr><tr> +<td class="tdl_top"></td> +<td class="tdc_top"><a id="6u">6</a></td> +<td class="tdl_top">\(B_1\)</td> +<td class="tdl_top">Recorded by H. H. Plaskett in 10 Lacertae</td> +</tr> + </tbody> +</table> + +<p><span class="pagenum" id="Page_208">[Pg 208]</span></p> +<p class="nindc space-above2"> +V. MATERIAL BEARING ON THE CLASSIFICATION OF \(A\) STARS, QUOTED IN +CHAPTER XII</p> + + +<p class="nind"> +IN illustration of the problem of Class \(A\), observations of +sixty-two stars are collected in the following table. Successive +columns contain the H.D. number, the name of the star, the apparent +magnitude, the reduced proper motion \(H\), and the spectral class. +Then follow columns which indicate the presence (\(x\)) or absence of +metallic lines, the quality of the lines (sharp lines being represented +by the letter \(s\) and hazy lines by the letter \(h\)), the presence +of wings to the hydrogen lines, and the strength of the Sr+ line at +4077 and the Si+ lines at 4128, 4131.</p> + +<p><span class="pagenum" id="Page_209">[Pg 209]</span></p> + +<p>The stars in each class are arranged in order of increasing strength +of metallic lines, and it will be seen that this feature is correlated +with the strength of the silicon and strontium lines, but not with the +line quality or the hydrogen wings, nor with the reduced proper motion.</p> + +<h2><a id="TABLE_XXXIV">TABLE XXXIV</a></h2> + +<table class="autotable"> +<thead><tr> +<th class="tdc bb bt2 br"> H. D. </th> +<th class="tdc bb bt2 br" colspan="2"> Star </th> +<th class="tdc bb bt2 br"> m </th> +<th class="tdc bb bt2 br"> H </th> +<th class="tdc bb bt2 br"> Class </th> +<th class="tdc bb bt2 br"> Metalic<br> +Lines</th> +<th class="tdc bb bt2 br"> Line<br> +Quality</th> +<th class="tdc bb bt2 br"> H<br> +wings</th> +<th class="tdc bb bt2 br"> Sr+ </th> +<th class="tdc bb bt2"> Si+ </th> +</tr> +</thead> +<tbody><tr> +<td class="tdc br">120198</td> +<td class="tdl">84</td> +<td class="tdc br">UMa</td> +<td class="tdc br">5.53</td> +<td class="tdc br">6.4</td> +<td class="tdc br">\(A_{0p}\)</td> +<td class="tdc br">x</td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br">9</td> +<td class="tdc">10</td> +</tr><tr> +<td class="tdc br">108662</td> +<td class="tdl">17</td> +<td class="tdc br">Com</td> +<td class="tdc br">5.38</td> +<td class="tdc br">2.7</td> +<td class="tdc br">\(A_{0p}\)</td> +<td class="tdc br">x</td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br">7</td> +<td class="tdc">8</td> +</tr><tr> +<td class="tdc br">170397</td> +<td class="tdl">Br</td> +<td class="tdc br">2314</td> +<td class="tdc br">5.99</td> +<td class="tdc br">2.7</td> +<td class="tdc br">\(A_{0p}\)</td> +<td class="tdc br">x</td> +<td class="tdc br">h</td> +<td class="tdc br"></td> +<td class="tdc br">6</td> +<td class="tdc">9</td> +</tr><tr> +<td class="tdc br">133029</td> +<td class="tdl">+47°</td> +<td class="tdc br">2192</td> +<td class="tdc br">6.16</td> +<td class="tdc br">-</td> +<td class="tdc br">\(A_{0p}\)</td> +<td class="tdc br">x</td> +<td class="tdc br">h</td> +<td class="tdc br"></td> +<td class="tdc br">5</td> +<td class="tdc">11</td> +</tr><tr> +<td class="tdc br">140160</td> +<td class="tdl">\(\chi\)</td> +<td class="tdc br">Ser</td> +<td class="tdc br">5.26</td> +<td class="tdc br">3.5</td> +<td class="tdc br">\(A_{0p}\)</td> +<td class="tdc br">x</td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br">10</td> +<td class="tdc">5</td> +</tr><tr> +<td class="tdc br">94334</td> +<td class="tdl">\(\varpi\)</td> +<td class="tdc br">Uma</td> +<td class="tdc br">4.34</td> +<td class="tdc br">3.6</td> +<td class="tdc br">\(A_0\)</td> +<td class="tdc br">x</td> +<td class="tdc br">s</td> +<td class="tdc br"></td> +<td class="tdc br">2</td> +<td class="tdc">3</td> +</tr><tr> +<td class="tdc br">58142</td> +<td class="tdl">21</td> +<td class="tdc br">Lyn</td> +<td class="tdc br">4.45</td> +<td class="tdc br">2.9</td> +<td class="tdc br">\(A_0\)</td> +<td class="tdc br"></td> +<td class="tdc br">h</td> +<td class="tdc br"></td> +<td class="tdc br">-</td> +<td class="tdc">4</td> +</tr><tr> +<td class="tdc br">192913</td> +<td class="tdl">+27°</td> +<td class="tdc br">3668</td> +<td class="tdc br">6.69</td> +<td class="tdc br">-</td> +<td class="tdc br">\(A_{0p}\)</td> +<td class="tdc br"></td> +<td class="tdc br">h</td> +<td class="tdc br"></td> +<td class="tdc br">?</td> +<td class="tdc">7</td> +</tr><tr> +<td class="tdc br">225132</td> +<td class="tdl">2</td> +<td class="tdc br">Cet</td> +<td class="tdc br">4.62</td> +<td class="tdc br">1.2</td> +<td class="tdc br">\(A_0\)</td> +<td class="tdc br"></td> +<td class="tdc br">h</td> +<td class="tdc br"></td> +<td class="tdc br">-</td> +<td class="tdc">4</td> +</tr><tr> +<td class="tdc br">41841</td> +<td class="tdl">89</td> +<td class="tdc br">Lep</td> +<td class="tdc br">5.50</td> +<td class="tdc br">2.2</td> +<td class="tdc br">\(A_0\)</td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br">-</td> +<td class="tdc">-</td> +</tr><tr> +<td class="tdc br">222661</td> +<td class="tdl">\(\varpi^2\)</td> +<td class="tdc br">Aqr</td> +<td class="tdc br">4.62</td> +<td class="tdc br">4.8</td> +<td class="tdc br">\(A_0\)</td> +<td class="tdc br"></td> +<td class="tdc br">h</td> +<td class="tdc br"></td> +<td class="tdc br">-</td> +<td class="tdc">-</td> +</tr><tr> +<td class="tdc br">87887</td> +<td class="tdl">15</td> +<td class="tdc br">Sex</td> +<td class="tdc br">4.6</td> +<td class="tdc br">1.9</td> +<td class="tdc br">\(A_0\)</td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br">-</td> +<td class="tdc">5</td> +</tr><tr> +<td class="tdc br">213323</td> +<td class="tdl">38</td> +<td class="tdc br">Peg</td> +<td class="tdc br">5.51</td> +<td class="tdc br">3.3</td> +<td class="tdc br">\(A_0\)</td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br">-</td> +<td class="tdc">-</td> +</tr><tr> +<td class="tdc br">25642</td> +<td class="tdl">\(\lambda\)</td> +<td class="tdc br">Per</td> +<td class="tdc br">4.33</td> +<td class="tdc br">2.2</td> +<td class="tdc br">\(A_0\)</td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br">-</td> +<td class="tdc">4</td> +</tr><tr> +<td class="tdc br">114330</td> +<td class="tdl">\(\theta\)</td> +<td class="tdc br">Vir</td> +<td class="tdc br">4.44</td> +<td class="tdc br">3.2</td> +<td class="tdc br">\(A_0\)</td> +<td class="tdc br"></td> +<td class="tdc br">s</td> +<td class="tdc br"></td> +<td class="tdc br">-</td> +<td class="tdc">3</td> +</tr><tr> +<td class="tdc br">109485</td> +<td class="tdl">23</td> +<td class="tdc br">Com</td> +<td class="tdc br">4.78</td> +<td class="tdc br">4.1</td> +<td class="tdc br">\(A_0\)</td> +<td class="tdc br"></td> +<td class="tdc br">s</td> +<td class="tdc br"></td> +<td class="tdc br">-</td> +<td class="tdc">3</td> +</tr><tr> +<td class="tdc br">103632</td> +<td class="tdl">\(\eta\)</td> +<td class="tdc br">Cra</td> +<td class="tdc br">5.16</td> +<td class="tdc br">3.8</td> +<td class="tdc br">\(A_0\)</td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br">x</td> +<td class="tdc br">-</td> +<td class="tdc">-</td> +</tr><tr> +<td class="tdc br">110411</td> +<td class="tdl">\(\rho\)</td> +<td class="tdc br">Vir</td> +<td class="tdc br">4.95</td> +<td class="tdc br">5.6</td> +<td class="tdc br">\(A_0\)</td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br">x</td> +<td class="tdc br">-</td> +<td class="tdc">-</td> +</tr><tr> +<td class="tdc br">133962</td> +<td class="tdl">k</td> +<td class="tdc br">Boo</td> +<td class="tdc br">5.59</td> +<td class="tdc br">4.6</td> +<td class="tdc br">\(A_0\)</td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br">x</td> +<td class="tdc br">-</td> +<td class="tdc">-</td> +</tr><tr> +<td class="tdc br">188260</td> +<td class="tdl">13</td> +<td class="tdc br">Vul</td> +<td class="tdc br">4.50</td> +<td class="tdc br">2.5</td> +<td class="tdc br">\(A_0\)</td> +<td class="tdc br"></td> +<td class="tdc br">h</td> +<td class="tdc br">x</td> +<td class="tdc br">-</td> +<td class="tdc">4</td> +</tr><tr> +<td class="tdc br">124224</td> +<td class="tdl">\(\pi\)</td> +<td class="tdc br">12</td> +<td class="tdc br">4.90</td> +<td class="tdc br">3.8</td> +<td class="tdc br">\(A_{0p}\)</td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br">-</td> +<td class="tdc">11</td> +</tr><tr> +<td class="tdc br">183056</td> +<td class="tdl">4</td> +<td class="tdc br">Cyg</td> +<td class="tdc br">5.2</td> +<td class="tdc br">-0.4</td> +<td class="tdc br">\(A_{0p}\)</td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br">-</td> +<td class="tdc">9</td> +</tr><tr> +<td class="tdc br">183986</td> +<td class="tdl">+35°</td> +<td class="tdc br">3658</td> +<td class="tdc br">6.04</td> +<td class="tdc br">-</td> +<td class="tdc br">\(A_{0p}\)</td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br">x</td> +<td class="tdc br">-</td> +<td class="tdc">5</td> +</tr><tr> +<td class="tdc br"></td> +<td class="tdl"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc"></td> +</tr><tr> +<td class="tdc br">196502</td> +<td class="tdl">73</td> +<td class="tdc br">Dra</td> +<td class="tdc br">5.18</td> +<td class="tdc br">1.2</td> +<td class="tdc br">\(A_2\)</td> +<td class="tdc br">x</td> +<td class="tdc br">s</td> +<td class="tdc br"></td> +<td class="tdc br">12</td> +<td class="tdc">10</td> +</tr><tr> +<td class="tdc br">148367</td> +<td class="tdl">\(\nu\)</td> +<td class="tdc br">Oph</td> +<td class="tdc br">4.68</td> +<td class="tdc br">4.3</td> +<td class="tdc br">\(A_2\)</td> +<td class="tdc br">x</td> +<td class="tdc br">s</td> +<td class="tdc br">x</td> +<td class="tdc br">9</td> +<td class="tdc">8</td> +</tr><tr> +<td class="tdc br">118022</td> +<td class="tdl">78</td> +<td class="tdc br">Vir</td> +<td class="tdc br">4.93</td> +<td class="tdc br">3.5</td> +<td class="tdc br">\(A_{2p}\)</td> +<td class="tdc br">x</td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br">10</td> +<td class="tdc">9</td> +</tr><tr> +<td class="tdc br">182564</td> +<td class="tdl">\(\pi\)</td> +<td class="tdc br">Dra</td> +<td class="tdc br">4.63</td> +<td class="tdc br">2.9</td> +<td class="tdc br">\(A_2\)</td> +<td class="tdc br">x</td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br">7</td> +<td class="tdc">7</td> +</tr><tr> +<td class="tdc br">125337</td> +<td class="tdl">\(\lambda\)</td> +<td class="tdc br">Vir</td> +<td class="tdc br">4.60</td> +<td class="tdc br">-1.9</td> +<td class="tdc br">\(A_2\)</td> +<td class="tdc br">x</td> +<td class="tdc br">h</td> +<td class="tdc br"></td> +<td class="tdc br">7</td> +<td class="tdc">6</td> +</tr><tr> +<td class="tdc br">214734</td> +<td class="tdl">30</td> +<td class="tdc br">Cep</td> +<td class="tdc br">5.21</td> +<td class="tdc br">1.6</td> +<td class="tdc br">\(A_2\)</td> +<td class="tdc br">x</td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br">3?</td> +<td class="tdc">5</td> +</tr><tr> +<td class="tdc br">7804</td> +<td class="tdl">89</td> +<td class="tdc br">Psc</td> +<td class="tdc br">5.28</td> +<td class="tdc br">4.2</td> +<td class="tdc br">\(A_2\)</td> +<td class="tdc br">x</td> +<td class="tdc br"></td> +<td class="tdc br">x</td> +<td class="tdc br">5</td> +<td class="tdc">7</td> +</tr><tr> +<td class="tdc br">220825</td> +<td class="tdl">\(\kappa\)</td> +<td class="tdc br">Psc</td> +<td class="tdc br">4.94</td> +<td class="tdc br">-</td> +<td class="tdc br">\(A_{2p}\)</td> +<td class="tdc br">x</td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br">6</td> +<td class="tdc">7</td> +</tr><tr> +<td class="tdc br">72968</td> +<td class="tdl">3</td> +<td class="tdc br">Hya</td> +<td class="tdc br">5.61</td> +<td class="tdc br">2.8</td> +<td class="tdc br">\(A_{2p}\)</td> +<td class="tdc br">x</td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br">6</td> +<td class="tdc">7</td> +</tr><tr> +<td class="tdc br">56405</td> +<td class="tdl">Paris</td> +<td class="tdc br">8971</td> +<td class="tdc br">5.39</td> +<td class="tdc br">4.7</td> +<td class="tdc br">\(A_2\)</td> +<td class="tdc br">x</td> +<td class="tdc br">s</td> +<td class="tdc br">s</td> +<td class="tdc br">3?</td> +<td class="tdc">6</td> +</tr><tr> +<td class="tdc br">20677</td> +<td class="tdl">32</td> +<td class="tdc br">Per</td> +<td class="tdc br">4.98</td> +<td class="tdc br">3.8</td> +<td class="tdc br">\(A_2\)</td> +<td class="tdc br">x</td> +<td class="tdc br"></td> +<td class="tdc br">x</td> +<td class="tdc br">-</td> +<td class="tdc">5 +<span class="pagenum" id="Page_210">[Pg 210]</span></td> +</tr><tr> +<td class="tdc br">48250</td> +<td class="tdl">12</td> +<td class="tdc br">Lyn</td> +<td class="tdc br">4.89</td> +<td class="tdc br">1.8</td> +<td class="tdc br">\(A_2\)</td> +<td class="tdc br">x</td> +<td class="tdc br"></td> +<td class="tdc br">x</td> +<td class="tdc br">-</td> +<td class="tdc">5</td> +</tr><tr> +<td class="tdc br">107612</td> +<td class="tdl">-</td> +<td class="tdc br">Com</td> +<td class="tdc br">6.56</td> +<td class="tdc br">-</td> +<td class="tdc br">\(A_{2p}\)</td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br">x</td> +<td class="tdc br">9</td> +<td class="tdc">-</td> +</tr><tr> +<td class="tdc br">18519,20</td> +<td class="tdl">\(\epsilon\)</td> +<td class="tdc br">Ari</td> +<td class="tdc br">4.6</td> +<td class="tdc br">1.1</td> +<td class="tdc br">\(A_2\),\(A_2\)</td> +<td class="tdc br"></td> +<td class="tdc br">s</td> +<td class="tdc br"></td> +<td class="tdc br">3</td> +<td class="tdc">3</td> +</tr><tr> +<td class="tdc br">107966</td> +<td class="tdl">13</td> +<td class="tdc br">Com</td> +<td class="tdc br">5.10</td> +<td class="tdc br">2.7</td> +<td class="tdc br">\(A_2\)</td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br">-</td> +<td class="tdc">-</td> +</tr><tr> +<td class="tdc br">108382</td> +<td class="tdl">16</td> +<td class="tdc br">Com</td> +<td class="tdc br">5.04</td> +<td class="tdc br">0.6</td> +<td class="tdc br">\(A_2\)</td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br">-</td> +<td class="tdc">-</td> +</tr><tr> +<td class="tdc br"></td> +<td class="tdl"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc"></td> +</tr><tr> +<td class="tdc br">108945</td> +<td class="tdl">21</td> +<td class="tdc br">Com</td> +<td class="tdc br">5.39</td> +<td class="tdc br">1.9</td> +<td class="tdc br">\(A_{3p}\)</td> +<td class="tdc br">x</td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br">11</td> +<td class="tdc">9</td> +</tr><tr> +<td class="tdc br">108642</td> +<td class="tdl">+26°</td> +<td class="tdc br">2138</td> +<td class="tdc br">6.48</td> +<td class="tdc br">-</td> +<td class="tdc br">\(A_3\)</td> +<td class="tdc br">x</td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br">8</td> +<td class="tdc">6</td> +</tr><tr> +<td class="tdc br">89904</td> +<td class="tdl">27</td> +<td class="tdc br">Lmi</td> +<td class="tdc br">6.1</td> +<td class="tdc br">3.0</td> +<td class="tdc br">\(A_3\)</td> +<td class="tdc br">x</td> +<td class="tdc br">h</td> +<td class="tdc br">x</td> +<td class="tdc br">6</td> +<td class="tdc">9</td> +</tr><tr> +<td class="tdc br">108651</td> +<td class="tdl">+26°</td> +<td class="tdc br">2353</td> +<td class="tdc br">6.69</td> +<td class="tdc br">-</td> +<td class="tdc br">\(A_3\)</td> +<td class="tdc br">x</td> +<td class="tdc br">h</td> +<td class="tdc br"></td> +<td class="tdc br">7</td> +<td class="tdc">6</td> +</tr><tr> +<td class="tdc br">170296</td> +<td class="tdl">\(\gamma\)</td> +<td class="tdc br">Scu</td> +<td class="tdc br">4.73</td> +<td class="tdc br">-0.5</td> +<td class="tdc br"></td> +<td class="tdc br">x</td> +<td class="tdc br">h</td> +<td class="tdc br">x</td> +<td class="tdc br">-</td> +<td class="tdc">7</td> +</tr><tr> +<td class="tdc br">115331</td> +<td class="tdl">196</td> +<td class="tdc br">Cen</td> +<td class="tdc br">6.0</td> +<td class="tdc br">3.4</td> +<td class="tdc br">\(A_{3p}\)</td> +<td class="tdc br"></td> +<td class="tdc br">h</td> +<td class="tdc br"></td> +<td class="tdc br">9</td> +<td class="tdc">-</td> +</tr><tr> +<td class="tdc br">108486</td> +<td class="tdl">+26°</td> +<td class="tdc br">2352</td> +<td class="tdc br">6.57</td> +<td class="tdc br">-</td> +<td class="tdc br">\(A_3\)</td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br">7</td> +<td class="tdc">-</td> +</tr><tr> +<td class="tdc br">104321</td> +<td class="tdl">\(\pi\)</td> +<td class="tdc br">Vir</td> +<td class="tdc br">4.57</td> +<td class="tdc br">2.2</td> +<td class="tdc br">\(A_3\)</td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br">5</td> +<td class="tdc">-</td> +</tr><tr> +<td class="tdc br"></td> +<td class="tdl"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc"></td> +</tr><tr> +<td class="tdc br">222345</td> +<td class="tdl">\(\varpi_1\)</td> +<td class="tdc br">Aqr</td> +<td class="tdc br">5.16</td> +<td class="tdc br">4.6</td> +<td class="tdc br">\(A_5\)</td> +<td class="tdc br">x</td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br">-</td> +<td class="tdc">9</td> +</tr><tr> +<td class="tdc br">14690</td> +<td class="tdl">70</td> +<td class="tdc br">Cet</td> +<td class="tdc br">5.62</td> +<td class="tdc br">4.3</td> +<td class="tdc br">\(A_5\)</td> +<td class="tdc br">x</td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br">7</td> +<td class="tdc">?</td> +</tr><tr> +<td class="tdc br">189849</td> +<td class="tdl">15</td> +<td class="tdc br">Vul</td> +<td class="tdc br">4.74</td> +<td class="tdc br">3.3</td> +<td class="tdc br">\(A_5\)</td> +<td class="tdc br">x</td> +<td class="tdc br">s</td> +<td class="tdc br">x</td> +<td class="tdc br">9</td> +<td class="tdc">6</td> +</tr><tr> +<td class="tdc br">28546</td> +<td class="tdl">81</td> +<td class="tdc br">Tau</td> +<td class="tdc br">5.49</td> +<td class="tdc br">5.7</td> +<td class="tdc br">\(A_5\)</td> +<td class="tdc br">x</td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br">9</td> +<td class="tdc">9</td> +</tr><tr> +<td class="tdc br">40536</td> +<td class="tdl">2</td> +<td class="tdc br">Mon</td> +<td class="tdc br">5.10</td> +<td class="tdc br">4.0</td> +<td class="tdc br">\(A_5\)</td> +<td class="tdc br">x</td> +<td class="tdc br">h?</td> +<td class="tdc br"></td> +<td class="tdc br">7</td> +<td class="tdc">7</td> +</tr><tr> +<td class="tdc br">15089</td> +<td class="tdl">\(\iota\)</td> +<td class="tdc br">Cas</td> +<td class="tdc br">4.59</td> +<td class="tdc br">0.5</td> +<td class="tdc br">\(A_{5p}\)</td> +<td class="tdc br">x</td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br">12</td> +<td class="tdc">9</td> +</tr><tr> +<td class="tdc br">91312</td> +<td class="tdl">Gr</td> +<td class="tdc br">1658</td> +<td class="tdc br">4.85</td> +<td class="tdc br">5.6</td> +<td class="tdc br">\(A_5\)</td> +<td class="tdc br">x</td> +<td class="tdc br">s</td> +<td class="tdc br">x</td> +<td class="tdc br">5</td> +<td class="tdc">6</td> +</tr><tr> +<td class="tdc br">159560</td> +<td class="tdl">\(\nu^2\)</td> +<td class="tdc br">Dra</td> +<td class="tdc br">4.95</td> +<td class="tdc br">6.0</td> +<td class="tdc br">\(A_5\)</td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br">8</td> +<td class="tdc">-</td> +</tr><tr> +<td class="tdc br"></td> +<td class="tdl"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc"></td> +</tr><tr> +<td class="tdc br">90277</td> +<td class="tdl">30</td> +<td class="tdc br">Lmi</td> +<td class="tdc br">4.85</td> +<td class="tdc br">5.0</td> +<td class="tdc br">\(F_0\)</td> +<td class="tdc br">x</td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br">9</td> +<td class="tdc">9</td> +</tr><tr> +<td class="tdc br">57749</td> +<td class="tdl">\(\pi\)</td> +<td class="tdc br">86</td> +<td class="tdc br">5.83</td> +<td class="tdc br">2.3</td> +<td class="tdc br">\(F_0\)</td> +<td class="tdc br">x</td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br">9</td> +<td class="tdc">6</td> +</tr><tr> +<td class="tdc br">92787</td> +<td class="tdl">\(\pi\)</td> +<td class="tdc br">135</td> +<td class="tdc br">5.28</td> +<td class="tdc br">7.6</td> +<td class="tdc br">\(F_0\)</td> +<td class="tdc br">x</td> +<td class="tdc br">s</td> +<td class="tdc br"></td> +<td class="tdc br">9</td> +<td class="tdc">6</td> +</tr><tr> +<td class="tdc br">112429</td> +<td class="tdl">8</td> +<td class="tdc br">Dra</td> +<td class="tdc br">5.27</td> +<td class="tdc br">3.0</td> +<td class="tdc br">\(F_0\)</td> +<td class="tdc br">x</td> +<td class="tdc br"></td> +<td class="tdc br"></td> +<td class="tdc br">7</td> +<td class="tdc">7</td> +</tr><tr> +<td class="tdc br">28485</td> +<td class="tdl">80</td> +<td class="tdc br">Tau</td> +<td class="tdc br">5.70</td> +<td class="tdc br">5.8</td> +<td class="tdc br">\(F_0\)</td> +<td class="tdc br"></td> +<td class="tdc br">h</td> +<td class="tdc br"></td> +<td class="tdc br">6</td> +<td class="tdc">5</td> +</tr><tr> +<td class="tdc bb br">28677</td> +<td class="tdl bb">85</td> +<td class="tdc bb br">Tau</td> +<td class="tdc bb br">6.04</td> +<td class="tdc bb br">-</td> +<td class="tdc bb br">\(F_0\)</td> +<td class="tdc bb br">-</td> +<td class="tdc bb br"></td> +<td class="tdc bb br"></td> +<td class="tdc bb br">7</td> +<td class="tdc bb">-</td> +</tr> + </tbody> +</table> + + +<hr class="chap x-ebookmaker-drop"> + +<div class="chapter"> +<p><span class="pagenum" id="Page_211">[Pg 211]</span></p> + +<h2 class="nobreak" id="SUBJECT_INDEX">SUBJECT INDEX</h2> +</div> + +<ul class="index"> +<li class="ifrst">\(A\), Class <a href="#Page_166">166</a></li> +<li class="isub1">classification <a href="#Page_168">168</a></li> +<li class="isub1">metallic lines and band absorption <a href="#Page_167">167</a></li> +<li class="isub1">peculiar <a href="#Page_172">172</a></li> +<li class="isub1">observational material <a href="#Page_208">208</a></li> + +<li class="ifrst">Abnormal abundance, effect on</li> +<li class="isub1">spectrum <a href="#Page_172">172</a></li> + +<li class="ifrst">Abnormal conditions, effect on</li> +<li class="isub1">spectrum <a href="#Page_171">171</a></li> + +<li class="ifrst">Absent elements <a href="#Page_86">86</a></li> + +<li class="ifrst">Absolute magnitudes for Draper</li> +<li class="isub1">classes <a href="#Page_197">197</a></li> + +<li class="ifrst">Absorbing efficiencies of atoms <a href="#Page_136">136</a></li> + +<li class="ifrst">Absorption coefficient <a href="#Page_110">110</a></li> + +<li class="ifrst">Absorption lines <a href="#Page_11">11</a>, <a href="#Page_50">50</a></li> + +<li class="ifrst">Abundance of atomic species, <a href="#Page_135">135</a>, <a href="#Page_177">177</a>,</li> +<li class="isub1"><a href="#Page_183">183</a></li> + +<li class="ifrst">Abundance of atoms, terrestrial <a href="#Page_5">5</a></li> + +<li class="ifrst">Aluminum <a href="#Page_68">68</a>, <a href="#Page_122">122</a></li> + +<li class="ifrst">Arc spectrum <a href="#Page_13">13</a></li> + +<li class="ifrst"><a id="atomic_life">Atomic life</a> <a href="#Page_21">21</a>, <a href="#Page_110">110</a></li> +<li class="isub1">life, astrophysical <a href="#Page_22">22</a>, <a href="#Page_158">158</a></li> +<li class="isub1">nucleus <a href="#Page_4">4</a></li> +<li class="isub1">number <a href="#Page_5">5</a></li> +<li class="isub1">states, probabilities of <a href="#Page_23">23</a></li> +<li class="isub1">weights <a href="#Page_5">5</a></li> + +<li class="ifrst">Azimuthal quantum number <a href="#Page_8">8</a>, <a href="#Page_204">204</a></li> + +<li class="ifrst">Balmer lines in \(A\) stars <a href="#Page_166">166</a></li> +<li class="isub1">lines, maximum <a href="#Page_166">166</a></li> +<li class="isub1">series limit <a href="#Page_42">42</a></li> + +<li class="ifrst">Barium <a href="#Page_85">85</a>, <a href="#Page_126">126</a></li> + +<li class="ifrst">Blackness of continuous background <a href="#Page_49">49</a></li> + +<li class="ifrst">Blending of lines <a href="#Page_171">171</a></li> + +<li class="ifrst">Bohr’s Table <a href="#Page_9">9</a></li> + +<li class="ifrst">Boundary temperature <a href="#Page_27">27</a></li> + +<li class="ifrst">Calcium <a href="#Page_70">70</a>, <a href="#Page_122">122</a></li> + +<li class="ifrst">Carbon <a href="#Page_59">59</a>, <a href="#Page_121">121</a>, <a href="#Page_207">207</a></li> +<li class="isub1">compounds <a href="#Page_61">61</a></li> +<li class="isub1">spectroscopic and chemical valencies <a href="#Page_11">11</a></li> + +<li class="ifrst">Central intensities of spectrum lines <a href="#Page_51">51</a></li> + +<li class="ifrst">Central temperature <a href="#Page_27">27</a></li> + +<li class="ifrst">Chemical symbols <a href="#Page_5">5</a></li> + +<li class="ifrst">Chemical valency <a href="#Page_10">10</a></li> + +<li class="ifrst">Chromium <a href="#Page_77">77</a>, <a href="#Page_124">124</a></li> + +<li class="ifrst">Chromosphere <a href="#Page_35">35</a>, <a href="#Page_47">47</a>, <a href="#Page_159">159</a></li> + +<li class="ifrst">Classification, meaning of <a href="#Page_190">190</a></li> + +<li class="ifrst">Classification, principles of <a href="#Page_191">191</a></li> + +<li class="ifrst">Cobalt <a href="#Page_80">80</a></li> + +<li class="ifrst">Color indices of stars <a href="#Page_49">49</a></li> + +<li class="ifrst">Conductivities of flames <a href="#Page_112">112</a></li> + +<li class="ifrst">Consistency of temperature scale <a href="#Page_130">130</a></li> + +<li class="ifrst">Continuous background of stellar</li> +<li class="isub1">spectrum <a href="#Page_46">46</a>, <a href="#Page_48">48</a></li> + +<li class="ifrst">Copper <a href="#Page_80">80</a></li> + +<li class="ifrst">Critical potential <a href="#Page_14">14</a></li> + +<li class="ifrst">Critical potential, astrophysical</li> +<li class="isub1">determination <a href="#Page_156">156</a></li> + +<li class="ifrst">c-stars <a href="#Page_173">173</a></li> + +<li class="ifrst">Definitions, index to <a href="#Page_203">203</a></li> + +<li class="ifrst">Density and radius of second type</li> +<li class="isub1">stars <a href="#Page_36">36</a></li> + +<li class="ifrst">Displacement rule <a href="#Page_13">13</a>, <a href="#Page_20">20</a></li> + +<li class="ifrst">Draper classes, homogeneity <a href="#Page_193">193</a></li> + +<li class="ifrst">Draper system <a href="#Page_191">191</a></li> + +<li class="ifrst">Duration of atomic states <a href="#Page_21">21</a></li> + +<li class="ifrst">Earth, composition of crust <a href="#Page_185">185</a></li> +<li class="isub1">origin of <a href="#Page_185">185</a></li> +<li class="isub1">total, composition of <a href="#Page_187">187</a></li> + +<li class="ifrst">Effective level <a href="#Page_28">28</a>, <a href="#Page_136">136</a></li> + +<li class="ifrst">Effective temperature <a href="#Page_27">27</a></li> + +<li class="ifrst">Effective temperature, Draper</li> +<li class="isub1">classes <a href="#Page_197">197</a></li> + +<li class="ifrst">Effect of conditions on spectrum <a href="#Page_24">24</a></li> + +<li class="ifrst">Electrons, extra-nuclear <a href="#Page_8">8</a></li> + +<li class="ifrst">Electron transfer <a href="#Page_11">11</a></li> + +<li class="ifrst">Elements <a href="#Page_5">5</a></li> + +<li class="ifrst">Elements, in stellar atmospheres <a href="#Page_55">55</a></li> + +<li class="ifrst">Emission lines, production of <a href="#Page_11">11</a>, <a href="#Page_53">53</a></li> + +<li class="ifrst">Emission lines, stars showing <a href="#Page_53">53</a></li> + +<li class="ifrst">Energy distribution in solar spectrum <a href="#Page_49">49</a></li> + +<li class="ifrst">Energy distribution in stellar</li> +<li class="isub1">spectrum <a href="#Page_49">49</a></li> + +<li class="ifrst">Equivalent outer orbits, electronic <a href="#Page_10">10</a></li> + +<li class="ifrst">Even number rule <a href="#Page_177">177</a></li> + +<li class="ifrst">Excitation <a href="#Page_11">11</a></li> + +<li class="ifrst">Excitation potential <a href="#Page_15">15</a></li> + +<li class="isub1"><span class="pagenum" id="Page_212">[Pg 212]</span></li> + +<li class="ifrst">Flash spectrum <a href="#Page_40">40</a>, <a href="#Page_53">53</a></li> + +<li class="ifrst">Formulae in theory of ionization <a href="#Page_106">106</a></li> + +<li class="ifrst">Fractional concentration <a href="#Page_105">105</a></li> + +<li class="ifrst">Furnace experiments <a href="#Page_112">112</a></li> + +<li class="ifrst">Galactic concentrations of Draper</li> +<li class="isub1">classes <a href="#Page_197">197</a></li> + +<li class="ifrst">Gallium <a href="#Page_81">81</a></li> + +<li class="ifrst">Gaseous nebulae, continuous</li> +<li class="isub1">spectrum <a href="#Page_49">49</a></li> + +<li class="ifrst">Giant and dwarf spectra <a href="#Page_195">195</a></li> + +<li class="ifrst">Giant and dwarf temperature</li> +<li class="isub1">differences <a href="#Page_31">31</a></li> + +<li class="ifrst">Helium <a href="#Page_58">58</a>, <a href="#Page_121">121</a></li> + +<li class="ifrst">Hot spark <a href="#Page_18">18</a></li> + +<li class="ifrst">Hydrogen, atom <a href="#Page_12">12</a></li> +<li class="isub1">continuous spectrum <a href="#Page_57">57</a></li> +<li class="isub1">energy levels <a href="#Page_13">13</a></li> +<li class="isub1">line intensities <a href="#Page_121">121</a></li> +<li class="isub1">peculiar behavior <a href="#Page_56">56</a></li> +<li class="isub1">secondary spectrum <a href="#Page_56">56</a></li> +<li class="isub1">stellar spectra <a href="#Page_55">55</a></li> + +<li class="ifrst">Inner quantum number <a href="#Page_204">204</a></li> + +<li class="ifrst">Ionization <a href="#Page_11">11</a>, <a href="#Page_15">15</a>, <a href="#Page_97">97</a></li> +<li class="isub1">as criterion of pressure <a href="#Page_44">44</a></li> +<li class="isub1">potential <a href="#Page_15">15</a></li> +<li class="isub1"><span style="margin-left: 2em;">"</span><span style="margin-left: 2em;"> </span>and atomic number <a href="#Page_20">20</a></li> +<li class="isub1"><span style="margin-left: 2em;">"</span><span style="margin-left: 2em;"> </span>astrophysical <a href="#Page_156">156</a></li> +<li class="isub1"><span style="margin-left: 2em;">"</span><span style="margin-left: 2em;"> </span>and temperature of</li> +<li class="isub1">maximum <a href="#Page_157">157</a></li> +<li class="isub1">temperature <a href="#Page_30">30</a></li> +<li class="isub1">temperature scale <a href="#Page_33">33</a>, <a href="#Page_132">132</a>, <a href="#Page_133">133</a></li> + +<li class="ifrst">Ionized atom, lines of <a href="#Page_101">101</a></li> + +<li class="ifrst">Intensity of lines <a href="#Page_23">23</a>, <a href="#Page_116">116</a></li> +<li class="isub1">accuracy <a href="#Page_118">118</a></li> +<li class="isub1">estimation <a href="#Page_117">117</a></li> +<li class="isub1">observational material <a href="#Page_116">116</a></li> + +<li class="ifrst">Intensity scales <a href="#Page_117">117</a></li> + +<li class="ifrst">Interior of star, ionization in <a href="#Page_18">18</a></li> + +<li class="ifrst">Iron <a href="#Page_79">79</a>, <a href="#Page_125">125</a></li> + +<li class="ifrst">Isotopes <a href="#Page_5">5</a></li> + +<li class="ifrst">Law of Mass Action <a href="#Page_105">105</a>, <a href="#Page_110">110</a></li> + +<li class="ifrst">Lead <a href="#Page_86">86</a></li> + +<li class="ifrst">Level of origin of lines <a href="#Page_134">134</a></li> + +<li class="ifrst">Life of atom <a href="#Page_21">21</a></li> + +<li class="ifrst">Life of atom, astrophysical <a href="#Page_22">22</a>, <a href="#Page_158">158</a></li> + +<li class="ifrst">Limit of Balmer series <a href="#Page_42">42</a></li> + +<li class="ifrst">Line intensity, data on <a href="#Page_121">121</a></li> +<li class="isub1">notes on <a href="#Page_127">127</a></li> +<li class="isub1">unknown lines <a href="#Page_207">207</a></li> + +<li class="ifrst">Lines of unknown origin <a href="#Page_55">55</a></li> + +<li class="ifrst">Lithium <a href="#Page_59">59</a></li> + +<li class="ifrst">Low temperature conditions, stellar</li> +<li class="isub1">atmosphere <a href="#Page_94">94</a></li> + +<li class="ifrst">Magnesium <a href="#Page_67">67</a>, <a href="#Page_122">122</a></li> + +<li class="ifrst">Magnesium, compounds <a href="#Page_68">67</a></li> + +<li class="ifrst">Manganese <a href="#Page_78">78</a>, <a href="#Page_124">124</a></li> + +<li class="ifrst">Marginal appearance <a href="#Page_105">105</a>, <a href="#Page_135">135</a>, <a href="#Page_179">179</a></li> + +<li class="ifrst">Marginal appearance, observational</li> +<li class="isub1">data <a href="#Page_181">181</a></li> + +<li class="ifrst">Mass numbers of isotopes <a href="#Page_5">5</a></li> + +<li class="ifrst">Maximum of lines <a href="#Page_106">106</a></li> + +<li class="ifrst">Meteorites, composition <a href="#Page_187">187</a></li> + +<li class="ifrst">Molecule, ionization of <a href="#Page_19">19</a></li> + +<li class="ifrst">Molybdenum <a href="#Page_84">84</a></li> + +<li class="ifrst">Nickel <a href="#Page_80">80</a></li> + +<li class="ifrst">Niobium <a href="#Page_84">84</a></li> + +<li class="ifrst">Nitrogen <a href="#Page_63">63</a>, <a href="#Page_207">207</a></li> + +<li class="ifrst">Nucleus, atomic <a href="#Page_4">4</a></li> + +<li class="ifrst">\(O\), Class <a href="#Page_162">162</a></li> + +<li class="ifrst">Occurrence of elements in stars <a href="#Page_5">5</a></li> + +<li class="ifrst">Optical depth <a href="#Page_27">27</a>, <a href="#Page_35">35</a></li> + +<li class="ifrst">Origin of line spectra <a href="#Page_11">11</a></li> + +<li class="ifrst">Orion nebula, continuous spectrum <a href="#Page_49">49</a></li> + +<li class="ifrst">Oxygen <a href="#Page_65">65</a>, <a href="#Page_207">207</a></li> + +<li class="ifrst">Oxygen, compounds <a href="#Page_66">66</a></li> + +<li class="ifrst">Palladium <a href="#Page_84">84</a></li> + +<li class="ifrst">Partial electron pressure <a href="#Page_109">109</a></li> + +<li class="ifrst">Partition function <a href="#Page_107">107</a></li> + +<li class="ifrst">Percentage of stars in Draper classes <a href="#Page_197">197</a></li> + +<li class="ifrst">Photosphere <a href="#Page_35">35</a>, <a href="#Page_47">47</a></li> + +<li class="ifrst">Photoelectric ionization <a href="#Page_159">159</a></li> + +<li class="ifrst">Physical constants, astrophysical</li> +<li class="isub1">evaluation <a href="#Page_155">155</a></li> + +<li class="ifrst">Physical constants, required by</li> +<li class="isub1">ionization theory <a href="#Page_108">108</a></li> + +<li class="ifrst">Potassium <a href="#Page_70">70</a></li> + +<li class="ifrst">Pressure, atmospheres of stars <a href="#Page_25">25</a>, <a href="#Page_34">34</a></li> +<li class="isub1">from Balmer series limit <a href="#Page_44">44</a></li> +<li class="isub1">from flash spectrum <a href="#Page_40">40</a></li> +<li class="isub1">from ionization theory <a href="#Page_45">45</a></li> +<li class="isub1">from line sharpness <a href="#Page_38">38</a></li> +<li class="isub1">from line width <a href="#Page_39">39</a></li> +<li class="isub1">from radiative equilibrium <a href="#Page_40">40</a></li> +<li class="isub1">shift of lines <a href="#Page_26">26</a>, <a href="#Page_38">38</a></li> +<li class="isub1">summary <a href="#Page_45">45</a></li> +<li class="isub1">gradient in outer layers of star <a href="#Page_34">34</a></li> + +<li class="ifrst">Quantum number <a href="#Page_8">8</a></li> + +<li class="ifrst">Quantum relation <a href="#Page_11">11</a></li> + +<li class="isub1"><span class="pagenum" id="Page_213">[Pg 213]</span></li> + +<li class="ifrst">Radiative equilibrium in outer layers</li> +<li class="isub1">of star <a href="#Page_40">40</a></li> + +<li class="ifrst">Radium <a href="#Page_86">86</a></li> + +<li class="ifrst">Radius and density of second type</li> +<li class="isub1">stars <a href="#Page_36">36</a></li> + +<li class="ifrst">Rare earths <a href="#Page_85">85</a></li> + +<li class="ifrst">Relative abundance of atoms,</li> +<li class="isub1">estimation <a href="#Page_183">183</a></li> +<li class="isub1">abundance of atoms in stellar</li> +<li class="isub1">atmosphere <a href="#Page_177">177</a></li> +<li class="isub1">intensities of spectrum lines <a href="#Page_23">23</a></li> + +<li class="ifrst">Reorganization time, <i>see</i> <a href="#atomic_life">atomic life</a></li> + +<li class="ifrst">Residual intensity <a href="#Page_51">51</a></li> + +<li class="ifrst">Reversing layer <a href="#Page_50">50</a></li> + +<li class="ifrst">Reversing layer, mass and</li> +<li class="isub1">dimensions <a href="#Page_47">47</a></li> + +<li class="ifrst">Rhodium <a href="#Page_84">84</a></li> + +<li class="ifrst">Rubidium <a href="#Page_81">81</a></li> + +<li class="ifrst">Ruthenium <a href="#Page_84">84</a></li> + +<li class="ifrst">Rydberg constant <a href="#Page_14">14</a>, <a href="#Page_155">155</a>, <a href="#Page_204">204</a></li> + +<li class="ifrst">Saturation <a href="#Page_52">52</a>, <a href="#Page_135">135</a></li> + +<li class="ifrst">Scandium <a href="#Page_72">72</a>, <a href="#Page_123">123</a></li> + +<li class="ifrst">Series notation <a href="#Page_55">55</a></li> + +<li class="ifrst">Silicon <a href="#Page_24">24</a>, <a href="#Page_68">68</a>, <a href="#Page_122">122</a></li> + +<li class="ifrst">Silicon stars <a href="#Page_169">169</a></li> + +<li class="ifrst">Silver <a href="#Page_84">84</a></li> + +<li class="ifrst">Sodium <a href="#Page_67">67</a></li> + +<li class="ifrst">Sodium atom <a href="#Page_8">8</a></li> + +<li class="ifrst">Solar atmosphere <a href="#Page_47">47</a></li> +<li class="isub1">energy distribution <a href="#Page_49">49</a></li> +<li class="isub1">intensities <a href="#Page_113">113</a></li> + +<li class="ifrst">Space numbers for Draper classes <a href="#Page_197">197</a></li> + +<li class="ifrst">Spark spectrum <a href="#Page_14">14</a></li> + +<li class="ifrst">Special problems in stellar</li> +<li class="isub1">atmospheres <a href="#Page_161">161</a></li> + +<li class="ifrst"><a id="spectroscopic">Spectroscopic</a> valency electrons <a href="#Page_10">10</a></li> + +<li class="ifrst">Stark effect <a href="#Page_26">26</a></li> + +<li class="ifrst">Stars used for intensity estimates <a href="#Page_119">119</a></li> + +<li class="ifrst">Stellar atmosphere compared with</li> +<li class="isub1">earth’s crust <a href="#Page_184">184</a></li> + +<li class="ifrst">Stellar reversing layer <a href="#Page_91">91</a></li> + +<li class="ifrst">Strontium <a href="#Page_81">81</a>, <a href="#Page_126">126</a></li> + +<li class="ifrst">Strontium stars <a href="#Page_169">169</a></li> + +<li class="ifrst">Structure of absorption line <a href="#Page_180">180</a></li> + +<li class="ifrst">Subordinate lines <a href="#Page_12">12</a></li> + +<li class="ifrst">Subordinate series <a href="#Page_99">99</a></li> + +<li class="ifrst">Sulphur <a href="#Page_70">70</a>, <a href="#Page_207">207</a></li> + +<li class="ifrst">Surface gravity <a href="#Page_35">35</a>, <a href="#Page_36">36</a></li> + +<li class="ifrst">Symmetry number, <i>see</i> <a href="#spectroscopic">spectroscopic</a></li> +<li class="isub1">valency electrons</li> + +<li class="ifrst">Temperature class <a href="#Page_24">24</a>, <a href="#Page_112">112</a></li> +<li class="isub1">scale <a href="#Page_28">28</a>, <a href="#Page_33">33</a></li> +<li class="isub1">scale, ionization <a href="#Page_33">33</a>, <a href="#Page_133">133</a></li> +<li class="isub1">bright stars <a href="#Page_31">31</a></li> +<li class="isub1">giant and dwarf <a href="#Page_31">31</a></li> + +<li class="ifrst">Theory of solution <a href="#Page_110">110</a></li> + +<li class="ifrst">Tin <a href="#Page_85">85</a></li> + +<li class="ifrst">Titanium <a href="#Page_72">72</a>, <a href="#Page_123">123</a></li> + +<li class="ifrst">Titanium compounds <a href="#Page_75">75</a></li> + +<li class="ifrst">Total pressure in stellar atmospheres <a href="#Page_110">110</a></li> + +<li class="ifrst">Total quantum number <a href="#Page_8">8</a></li> + +<li class="ifrst">Typical giant star <a href="#Page_41">41</a></li> + +<li class="ifrst">Ultimate lines <a href="#Page_11">11</a>, <a href="#Page_94">94</a>, <a href="#Page_111">111</a></li> + +<li class="ifrst">Uniformity of stellar atmospheres <a href="#Page_178">178</a></li> + +<li class="ifrst">Valency, chemical <a href="#Page_10">10</a></li> + +<li class="ifrst">Valency, spectroscopic <a href="#Page_10">10</a></li> + +<li class="ifrst">Vanadium <a href="#Page_75">75</a>, <a href="#Page_124">124</a></li> + +<li class="ifrst">Weights of atomic states <a href="#Page_107">107</a></li> + +<li class="ifrst">Width of lines <a href="#Page_39">39</a></li> + +<li class="ifrst">Wings <a href="#Page_51">51</a></li> + +<li class="ifrst">Wolf-Rayet stars <a href="#Page_164">164</a></li> +<li class="isub1">absorption in <a href="#Page_164">164</a></li> +<li class="isub1">continuous spectrum <a href="#Page_49">49</a></li> + +<li class="ifrst">Yttrium <a href="#Page_82">82</a>, <a href="#Page_129">129</a></li> + +<li class="ifrst">Zeemann effect <a href="#Page_25">25</a></li> + +<li class="ifrst">Zinc <a href="#Page_80">80</a>, <a href="#Page_126">126</a></li> + +<li class="ifrst">Zirconium <a href="#Page_83">83</a></li> + +</ul> + + + +<hr class="chap x-ebookmaker-drop"> + +<div class="chapter"> +<p><span class="pagenum" id="Page_214">[Pg 214]</span></p> +<h2 class="nobreak" id="NAME_INDEX">NAME INDEX</h2> +</div> + +<ul class="index"> + +<li class="ifrst">Abbot <a href="#Page_30">30</a>, <a href="#Page_48">48</a>, <a href="#Page_51">51</a></li> + +<li class="ifrst">Adams <a href="#Page_54">54</a>, <a href="#Page_75">75</a>, <a href="#Page_140">140</a>, <a href="#Page_149">149</a>, <a href="#Page_192">192</a>, <a href="#Page_195">195</a></li> + +<li class="ifrst">Anderson <a href="#Page_26">26</a></li> + +<li class="ifrst">Aston <a href="#Page_5">5</a></li> + +<li class="ifrst">Babcock <a href="#Page_23">23</a>, <a href="#Page_38">38</a></li> + +<li class="ifrst">Baillaud <a href="#Page_48">48</a></li> + +<li class="ifrst">Baldet <a href="#Page_62">62</a></li> + +<li class="ifrst">Baxandall <a href="#Page_55">55</a>, <a href="#Page_63">63</a>, <a href="#Page_64">64</a>, <a href="#Page_149">149</a>, <a href="#Page_172">172</a>, <a href="#Page_173">173</a></li> + +<li class="ifrst">Belopolsky <a href="#Page_173">173</a></li> + +<li class="ifrst">Bohr <a href="#Page_8">8</a>, <a href="#Page_42">42</a>, <a href="#Page_108">108</a></li> + +<li class="ifrst">Bottlinger <a href="#Page_51">51</a></li> + +<li class="ifrst">Bowen <a href="#Page_18">18</a></li> + +<li class="ifrst">Brandt <a href="#Page_17">17</a></li> + +<li class="ifrst">Brill <a href="#Page_29">29</a></li> + +<li class="ifrst">Brooks <a href="#Page_68">68</a></li> + +<li class="ifrst">Brooksbank <a href="#Page_66">66</a></li> + +<li class="ifrst">Burns <a href="#Page_159">159</a></li> + +<li class="ifrst">Butler <a href="#Page_63">63</a></li> + +<li class="ifrst">Campbell, W. W. <a href="#Page_60">60</a>, <a href="#Page_163">163</a></li> + +<li class="ifrst">Cannon, A. J. <a href="#Page_54">54</a>, <a href="#Page_163">163</a>, <a href="#Page_190">190</a>, <a href="#Page_198">198</a></li> + +<li class="ifrst">Catalan <a href="#Page_17">17</a>, <a href="#Page_77">77</a>, <a href="#Page_84">84</a></li> + +<li class="ifrst">Chenault <a href="#Page_17">17</a></li> + +<li class="ifrst">Clarke, F. W. <a href="#Page_5">5</a>, <a href="#Page_184">184</a>, <a href="#Page_185">185</a>, <a href="#Page_187">187</a></li> + +<li class="ifrst">Coblentz <a href="#Page_30">30</a></li> + +<li class="ifrst">Compton, K. T. <a href="#Page_17">17</a>, <a href="#Page_56">56</a>, <a href="#Page_59">59</a></li> + +<li class="ifrst">Cortie <a href="#Page_66">66</a></li> + +<li class="ifrst">Coster <a href="#Page_23">23</a></li> + +<li class="ifrst">Curtis <a href="#Page_159">159</a></li> + +<li class="ifrst">Curtiss <a href="#Page_58">58</a></li> + +<li class="ifrst">Davies <a href="#Page_17">17</a>, <a href="#Page_19">19</a></li> + +<li class="ifrst">de Forcrand <a href="#Page_60">60</a></li> + +<li class="ifrst">de Gramont <a href="#Page_59">59</a>, <a href="#Page_111">111</a></li> + +<li class="ifrst">Dempster <a href="#Page_22">22</a></li> + +<li class="ifrst">Deslandres <a href="#Page_58">58</a></li> + +<li class="ifrst">Dorgelo <a href="#Page_23">23</a></li> + +<li class="ifrst">Duffendack <a href="#Page_19">19</a></li> + +<li class="ifrst">Dyson <a href="#Page_86">86</a></li> + +<li class="ifrst">Eddington <a href="#Page_27">27</a>, <a href="#Page_34">34</a>, <a href="#Page_41">41</a>, <a href="#Page_53">53</a>, <a href="#Page_180">180</a></li> + +<li class="ifrst">Einstein <a href="#Page_23">23</a>, <a href="#Page_113">113</a>, <a href="#Page_163">163</a></li> + +<li class="ifrst">Eldridge <a href="#Page_17">17</a></li> + +<li class="ifrst">Evershed <a href="#Page_26">26</a>, <a href="#Page_38">38</a>, <a href="#Page_58">58</a>, <a href="#Page_62">62</a></li> + +<li class="ifrst">Fairfield <a href="#Page_56">56</a>, <a href="#Page_57">57</a>, <a href="#Page_159">159</a></li> + +<li class="ifrst">Fermi <a href="#Page_23">23</a></li> + +<li class="ifrst">Foote <a href="#Page_17">17</a></li> + +<li class="ifrst">Fowler, A., <a href="#Page_11">11</a>, <a href="#Page_14">14</a>, <a href="#Page_17">17</a>, <a href="#Page_38">38</a>, <a href="#Page_56">56</a>, <a href="#Page_60">60</a>,</li> +<li class="isub1"><a href="#Page_62">62</a>, <a href="#Page_65">65</a>, <a href="#Page_66">66</a>, <a href="#Page_68">68</a>, <a href="#Page_75">75</a>, <a href="#Page_186">186</a>, <a href="#Page_191">191</a></li> + +<li class="ifrst">Fowler, R. H., <a href="#Page_17">17</a>, <a href="#Page_37">37</a>, <a href="#Page_44">44</a>, <a href="#Page_61">61</a>, <a href="#Page_70">70</a>,</li> +<li class="isub1"><a href="#Page_93">93</a>, <a href="#Page_106">106-110</a>, <a href="#Page_108">108</a>, <a href="#Page_133">133</a>, <a href="#Page_135">135</a>, <a href="#Page_156">156</a>, <a href="#Page_166">166</a>, <a href="#Page_179">179</a></li> + +<li class="ifrst">Franck <a href="#Page_19">19</a>, <a href="#Page_22">22</a>, <a href="#Page_43">43</a></li> + +<li class="ifrst">Füchtbauer <a href="#Page_23">23</a></li> + +<li class="ifrst">Gale <a href="#Page_75">75</a></li> + +<li class="ifrst">Giebeler <a href="#Page_86">86</a></li> + +<li class="ifrst">Gieseler <a href="#Page_17">17</a></li> + +<li class="ifrst">Gousmid <a href="#Page_86">86</a></li> + +<li class="ifrst">Grotrian <a href="#Page_17">17</a>, <a href="#Page_22">22</a></li> + +<li class="ifrst">Guckel <a href="#Page_60">60</a></li> + +<li class="ifrst">Hale <a href="#Page_25">25</a>, <a href="#Page_75">75</a></li> + +<li class="ifrst">Harper <a href="#Page_79">79</a>, <a href="#Page_117">117</a>, <a href="#Page_176">176</a>, <a href="#Page_192">192</a></li> + +<li class="ifrst">Harrison <a href="#Page_181">181</a></li> + +<li class="ifrst">Hartley <a href="#Page_81">81</a></li> + +<li class="ifrst">Hartmann <a href="#Page_71">71</a></li> + +<li class="ifrst">Hartree <a href="#Page_17">17</a>, <a href="#Page_61">61</a></li> + +<li class="ifrst">Heger <a href="#Page_67">67</a>, <a href="#Page_72">72</a></li> + +<li class="ifrst">Hertzsprung <a href="#Page_31">31</a>, <a href="#Page_175">175</a></li> + +<li class="ifrst">Hoffmann <a href="#Page_23">23</a></li> + +<li class="ifrst">Hopfield <a href="#Page_17">17</a>, <a href="#Page_186">186</a></li> + +<li class="ifrst">Horton <a href="#Page_17">17</a>, <a href="#Page_19">19</a></li> + +<li class="ifrst">Howe <a href="#Page_43">43</a></li> + +<li class="ifrst">Hubble <a href="#Page_49">49</a>, <a href="#Page_57">57</a></li> + +<li class="ifrst">Huggins <a href="#Page_57">57</a></li> + +<li class="ifrst">Hulburt <a href="#Page_26">26</a></li> + +<li class="ifrst">Huthsteiner <a href="#Page_17">17</a></li> + +<li class="ifrst">Jeffreys <a href="#Page_185">185</a></li> + +<li class="ifrst">Johnson, M. C. <a href="#Page_53">53</a>, <a href="#Page_85">85</a></li> + +<li class="ifrst">Johnson, R. C. <a href="#Page_62">62</a></li> + +<li class="ifrst">Joy <a href="#Page_54">54</a>, <a href="#Page_149">149</a>, <a href="#Page_192">192</a>, <a href="#Page_195">195</a></li> + +<li class="ifrst">Kiess, C. C. <a href="#Page_13">13</a>, <a href="#Page_17">17</a>, <a href="#Page_72">72</a>, <a href="#Page_84">84</a>, <a href="#Page_86">86</a>, <a href="#Page_173">173</a></li> + +<li class="ifrst">Kiess, H. K. <a href="#Page_17">17</a></li> + +<li class="ifrst">King, A. S. <a href="#Page_24">24</a>, <a href="#Page_38">38</a>, <a href="#Page_69">69</a>, <a href="#Page_84">84</a>, <a href="#Page_112">112</a></li> + +<li class="ifrst">King, E. S. <a href="#Page_29">29</a></li> + +<li class="ifrst">Knipping <a href="#Page_19">19</a></li> + +<li class="ifrst">Kohlschütter <a href="#Page_51">51</a>, <a href="#Page_140">140</a></li> + +<li class="ifrst">Kohn <a href="#Page_60">60</a></li> + +<li class="ifrst">Kossell <a href="#Page_13">13</a>, <a href="#Page_21">21</a></li> + +<li class="ifrst">Kramers <a href="#Page_8">8</a>, <a href="#Page_23">23</a></li> + +<li class="ifrst">Krüger <a href="#Page_19">19</a></li> + +<li class="isub1"><span class="pagenum" id="Page_215">[Pg 215]</span></li> + +<li class="ifrst">Landé <a href="#Page_25">25</a></li> + +<li class="ifrst">Lee <a href="#Page_71">71</a></li> + +<li class="ifrst">Lindblad <a href="#Page_48">48</a>, <a href="#Page_57">57</a>, <a href="#Page_62">62</a>, <a href="#Page_169">169</a></li> + +<li class="ifrst">Lindemann <a href="#Page_26">26</a></li> + +<li class="ifrst">Lockyer, J. N. <a href="#Page_64">64</a>, <a href="#Page_70">70</a>, <a href="#Page_172">172</a>, <a href="#Page_173">173</a></li> + +<li class="ifrst">Lundmark <a href="#Page_198">198</a></li> + +<li class="ifrst">Lunt <a href="#Page_6">6</a>, <a href="#Page_85">85</a></li> + +<li class="ifrst">Luyten <a href="#Page_67">67</a>, <a href="#Page_162">162</a>, <a href="#Page_170">170</a></li> + +<li class="ifrst">Lyman <a href="#Page_18">18</a>, <a href="#Page_57">57</a>, <a href="#Page_58">58</a></li> + +<li class="ifrst">Maury <a href="#Page_173">173</a></li> + +<li class="ifrst">McLennan <a href="#Page_18">18</a>, <a href="#Page_63">63</a></li> + +<li class="ifrst">Meggers <a href="#Page_13">13</a>, <a href="#Page_17">17</a>, <a href="#Page_72">72</a>, <a href="#Page_75">75</a>, <a href="#Page_82">82</a></li> + +<li class="ifrst">Menzel <a href="#Page_44">44</a>, <a href="#Page_66">66-68</a>, <a href="#Page_71">71</a>, <a href="#Page_74">74-76</a>, <a href="#Page_79">79-81</a>, <a href="#Page_85">85</a>,</li> +<li class="isub1"><a href="#Page_109">109</a>, <a href="#Page_116">116</a>, <a href="#Page_133">133</a>, <a href="#Page_166">166</a>, <a href="#Page_181">181</a></li> + +<li class="ifrst">Merrill, G. P. <a href="#Page_187">817</a></li> + +<li class="ifrst">Merrill, P. W. <a href="#Page_54">54</a>, <a href="#Page_83">83</a></li> + +<li class="ifrst">Merton <a href="#Page_25">25</a>, <a href="#Page_60">60</a>, <a href="#Page_62">62</a></li> + +<li class="ifrst">Mie <a href="#Page_22">22</a></li> + +<li class="ifrst">Millikan <a href="#Page_18">18</a></li> + +<li class="ifrst">Milne <a href="#Page_17">17</a>, <a href="#Page_22">22</a>, <a href="#Page_28">28</a>, <a href="#Page_36">36</a>, <a href="#Page_37">37</a>, <a href="#Page_44">44</a>, <a href="#Page_48">48</a>, <a href="#Page_50">50</a>, <a href="#Page_61">61</a>,</li> +<li class="isub1"><a href="#Page_70">70</a>, <a href="#Page_93">93</a>, <a href="#Page_97">97</a>, <a href="#Page_106">106-110</a>, <a href="#Page_113">113</a>, <a href="#Page_133">133</a>, <a href="#Page_135">135</a>, <a href="#Page_140">140</a>,</li> +<li class="isub1"><a href="#Page_156">156</a>, <a href="#Page_158">158</a>, <a href="#Page_166">166</a>, <a href="#Page_179">179</a></li> + +<li class="ifrst">Mitchell <a href="#Page_58">58</a>, <a href="#Page_86">86</a></li> + +<li class="ifrst">Mohler <a href="#Page_17">17</a></li> + +<li class="ifrst">Mulliken <a href="#Page_61">61</a></li> + +<li class="ifrst">Newall <a href="#Page_63">63</a></li> + +<li class="ifrst">Nicholson, J. W. <a href="#Page_43">43</a></li> + +<li class="ifrst">Noyes <a href="#Page_112">112</a></li> + +<li class="ifrst">Pannekoek <a href="#Page_35">35</a>, <a href="#Page_140">140</a></li> + +<li class="ifrst">Paschen <a href="#Page_14">14</a>, <a href="#Page_17">17</a>, <a href="#Page_156">156</a></li> + +<li class="ifrst">Payne <a href="#Page_20">20</a>, <a href="#Page_38">38</a>, <a href="#Page_43">43</a>, <a href="#Page_58">58</a>, <a href="#Page_60">60</a>, <a href="#Page_68">68</a>, <a href="#Page_156">156</a>,</li> +<li class="isub1"><a href="#Page_163">163</a>, <a href="#Page_183">183</a></li> + +<li class="ifrst">Plaskett, H. H. <a href="#Page_14">14</a>, <a href="#Page_30">30</a>, <a href="#Page_48">48</a>, <a href="#Page_51">51</a>, <a href="#Page_54">54</a>, <a href="#Page_59">59</a>,</li> +<li class="isub1"><a href="#Page_60">60</a>, <a href="#Page_64">64</a>, <a href="#Page_65">65</a>, <a href="#Page_85">85</a>, <a href="#Page_156">156</a>, <a href="#Page_163">163</a>, <a href="#Page_184">184</a></li> + +<li class="ifrst">Plaskett, J. S. <a href="#Page_60">60</a>, <a href="#Page_71">71</a>, <a href="#Page_162">162</a>, <a href="#Page_163">163</a>, <a href="#Page_171">171</a></li> + +<li class="ifrst">Pluvinel <a href="#Page_62">62</a></li> + +<li class="ifrst">Ramage <a href="#Page_81">81</a></li> + +<li class="ifrst">Rognley <a href="#Page_17">17</a></li> + +<li class="ifrst">Rosenberg <a href="#Page_29">29</a></li> + +<li class="ifrst">Rowland <a href="#Page_127">127</a></li> + +<li class="ifrst">Ruark <a href="#Page_17">17</a></li> + +<li class="ifrst">Rufus <a href="#Page_62">62</a>, <a href="#Page_72">72</a></li> + +<li class="ifrst">Russell <a href="#Page_17">17</a>, <a href="#Page_26">26</a>, <a href="#Page_37">37</a>, <a href="#Page_39">39</a>, <a href="#Page_40">40</a>, <a href="#Page_44">44</a>, <a href="#Page_47">47</a>,</li> +<li class="isub1"><a href="#Page_52">52</a>, <a href="#Page_55">55</a>, <a href="#Page_56">56</a>, <a href="#Page_59">59</a>, <a href="#Page_70">70</a>, <a href="#Page_79">79</a>, <a href="#Page_80">80</a>, <a href="#Page_110">110</a>, <a href="#Page_175">175</a>, <a href="#Page_178">178</a>,</li> +<li class="isub1"><a href="#Page_184">184</a>, <a href="#Page_203">203</a></li> + +<li class="ifrst">Saha <a href="#Page_43">43</a>, <a href="#Page_85">85</a>, <a href="#Page_105">105</a>, <a href="#Page_113">113</a></li> + +<li class="ifrst">St. John <a href="#Page_25">25</a>, <a href="#Page_38">38</a></li> + +<li class="ifrst">Sampson <a href="#Page_30">30</a></li> + +<li class="ifrst">Saunders <a href="#Page_38">38</a>, <a href="#Page_55">55</a>, <a href="#Page_203">203</a></li> + +<li class="ifrst">Scheiner <a href="#Page_29">29</a></li> + +<li class="ifrst">Schwarzschild <a href="#Page_51">51</a>, <a href="#Page_137">137</a>, <a href="#Page_160">160</a></li> + +<li class="ifrst">Seares <a href="#Page_31">31</a></li> + +<li class="ifrst">Shane <a href="#Page_62">62</a></li> + +<li class="ifrst">Shapley <a href="#Page_36">36</a>, <a href="#Page_40">40</a>, <a href="#Page_51">51</a>, <a href="#Page_62">62</a>, <a href="#Page_162">162</a>, <a href="#Page_168">168</a>,</li> +<li class="isub1"><a href="#Page_170">170</a>, <a href="#Page_185">185</a>, <a href="#Page_198">198</a></li> + +<li class="ifrst">Shaver <a href="#Page_17">17</a></li> + +<li class="ifrst">Shrum <a href="#Page_64">64</a></li> + +<li class="ifrst">Slipher <a href="#Page_75">75</a></li> + +<li class="ifrst">Smyth <a href="#Page_17">17</a>, <a href="#Page_19">19</a></li> + +<li class="ifrst">Sommerfeld <a href="#Page_13">13</a>, <a href="#Page_17">17</a>, <a href="#Page_21">21</a>, <a href="#Page_23">23</a></li> + +<li class="ifrst">Sponer <a href="#Page_17">17</a></li> + +<li class="ifrst">Stark <a href="#Page_25">25</a></li> + +<li class="ifrst">Stewart <a href="#Page_26">26</a>, <a href="#Page_37">37</a>, <a href="#Page_39">39</a>, <a href="#Page_40">40</a>, <a href="#Page_44">44</a>, <a href="#Page_47">47</a>, <a href="#Page_91">91</a>, <a href="#Page_110">110</a>, <a href="#Page_175">175</a></li> + +<li class="ifrst">Strutt <a href="#Page_66">66</a></li> + +<li class="ifrst">Takamine <a href="#Page_26">26</a></li> + +<li class="ifrst">Tate <a href="#Page_17">17</a></li> + +<li class="ifrst">Thomas <a href="#Page_18">18</a></li> + +<li class="ifrst">Turner <a href="#Page_22">22</a></li> + +<li class="ifrst">Udden <a href="#Page_17">17</a></li> + +<li class="ifrst">Urey <a href="#Page_108">108</a></li> + +<li class="ifrst">Van Maanen <a href="#Page_162">162</a></li> + +<li class="ifrst">Vegard <a href="#Page_63">63</a></li> + +<li class="ifrst">Violle <a href="#Page_60">60</a></li> + +<li class="ifrst">Von Zeipel <a href="#Page_185">185</a></li> + +<li class="ifrst">Walters <a href="#Page_13">13</a>, <a href="#Page_72">72</a>, <a href="#Page_77">77</a>, <a href="#Page_79">79</a></li> + +<li class="ifrst">Washington <a href="#Page_5">5</a>, <a href="#Page_184">184</a>, <a href="#Page_185">185</a></li> + +<li class="ifrst">Webb <a href="#Page_22">22</a></li> + +<li class="ifrst">Wien <a href="#Page_22">22</a></li> + +<li class="ifrst">Wilsing <a href="#Page_29">29</a>, <a href="#Page_48">48</a></li> + +<li class="ifrst">Wilson, E. B. <a href="#Page_162">162</a></li> + +<li class="ifrst">Wilson, H. A. <a href="#Page_112">112</a></li> + +<li class="ifrst">Wilson, H. H. <a href="#Page_162">162</a></li> + +<li class="ifrst">Woltjer <a href="#Page_113">113</a></li> + +<li class="ifrst">Wood <a href="#Page_22">22</a>, <a href="#Page_42">42</a>, <a href="#Page_57">57</a></li> + +<li class="ifrst">Wright <a href="#Page_43">43</a>, <a href="#Page_56">56</a>, <a href="#Page_57">57</a>, <a href="#Page_66">66</a>, <a href="#Page_163">163</a>, <a href="#Page_173">173</a></li> + +<li class="ifrst">Young <a href="#Page_79">79</a>, <a href="#Page_117">117</a>, <a href="#Page_176">176</a>, <a href="#Page_192">192</a></li> + +<li class="ifrst">Zeemann <a href="#Page_25">25</a></li> + +</ul> + + +</body> +</html> diff --git a/73996-src/README-math.txt b/73996-src/README-math.txt new file mode 100644 index 0000000..d7be885 --- /dev/null +++ b/73996-src/README-math.txt @@ -0,0 +1,115 @@ +MathJax HTML source file instructions +==================== +This project has math with high complexity equations (integrals, partial +derivatives, gradients, matrices, etc.), grouped equations, etc. The source is +a preliminary HTML file that uses MathJax to define mathematical expressions, +which is processed to generate a final HTML file, along with SVG images with +file names consisting of a number and “.svg”, such as “4.svg”. + +This source file is kept for the purpose of applying errata fixes. Although the +MathJax takes some learning, it is clearer than the generated final. This also +allows the SVG images to be regenerated with changes. + +Owing to the complexity of this type of book, it is not required to submit a +text file. + +Inline svg note +==================== +It is possible to use inline svg in the html file rather than images. It is +essential in this case also to keep the source file. + + +MathML note +==================== +For books with less complex math, this may be a good choice. It does not +require extra processing. + + +Tools +==================== +See the ppmath GitHub repository: + https://github.com/DistributedProofreaders/ppmath. +Follow the instructions to install m2svg. Don't forget to run "npm update -g" +before installing m2svg. + +Command line: + m2svg -i input.htm -o output.htm + +- The SVG files will be placed in a subdirectory of the working directory + called "images". + +- In the converted file, the maths expressions, delimited by the tags `\[` + and `\]` for *display* expressions or `\(` and `\)` for *inline* + expressions, are replaced by `<img>` links. + +- The "data-tex" attribute will contain the original maths expression. + + +Inline code example +==================== +For the expression AB^2 = AG × BD +the input + `\(\mathrm{AB}^{2} = \mathrm{AG} \times \mathrm{BD}\)` + +becomes + `<span class="nowrap"><img style="vertical-align: -0.186ex; width: 16.872ex; + height: 2.253ex;" src="images/4.svg" alt="" data-tex="\mathrm{AB}^{2} + = \mathrm{AG} \times \mathrm{BD}">,</span>` + +The file images/4.svg displays the desired expression. + + +Source files structure on Project Gutenberg +==================== +(eBook 75107 is used as an example) + +- 75107/ + - 75107-0.txt (optional) + - 75107-h/ + - 75107-h.htm (final HTML file) + - images/ (generated SVGs + other images) + - cover.jpg + - 1.svg + - (etc.) + - 75107-src/ + - 75107-src.htm (source HTML file with MathJax) + - README-math.txt (this file) + + +Submission process +==================== +- Generated final HTML and images should be submitted as normal. +- In addition, the source HTML will be included in a "source/" subdirectory. +- This readme will also be included in the "source/" subdirectory. + - Having it with the eBook makes it obvious, and avoids issues with + procedures changing in the future. +- The submitter should add a note that this is a MathJax project, and whether a + text file is included. +- Workflow will rename the source/ subdirectory and HTML file. + + +Errata process +==================== +(eBook 75107 is used as an example) + +1. Download the project files using Errata Workbench, and unzip. +2. Install m2svg if not already done. +3. Make the desired changes to 75107-src.htm. +4. Execute command line "m2svg -i 75107-src.htm -o 75107-h.htm". + - The image files will be placed in a subdirectory of the working directory + called "images". + - Check error report: filename_svgerr.err (as generated by Guiguts 2) + - Preview 75107-h.htm in a browser to make sure that all changes are properly + added. +5. Move 75107-h.htm to the 75107-h directory. +6. Move the contents of the images directory to the 75107-h/images directory. + - The generated images are just a number with .svg extension. There could be + other svg files which are not generated by m2svg. It is best to remove the + existing generated files from 75107-h/images first. + - Any non-generated images should be kept. Otherwise, if the edit results in + there being fewer generated images than before, some old ones could be left + behind. +7. Remove the generated images subdirectory and any other temporary files. +8. Run PPhtml from Guiguts 2 or Post-Processing Workbench to verify all images + are used, and none are missing. +9. Zip the project directory and upload to Errata Workbench. |