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<p class="nindc space-above2 space-below2">
STELLAR ATMOSPHERES
</p>


<hr class="chap x-ebookmaker-drop">

<div class="chapter">
<p class="nindc space-above2 space-below2">
HARVARD OBSERVATORY MONOGRAPHS<br>
<span class="allsmcap">HARLOW SHAPLEY, EDITOR</span></p>

<p class="nindc space-above2 space-below2">No. 1</p>




<h1>STELLAR ATMOSPHERES</h1>

<p class="nindc space-above2 space-below2">
A CONTRIBUTION TO THE OBSERVATIONAL
STUDY OF HIGH TEMPERATURE IN THE
REVERSING LAYERS OF STARS</p>




<p class="nindc space-above2 space-below2"><span class="allsmcap">BY</span></p>

<p class="nindc"><span class="large">CECILIA H. 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">&nbsp;&nbsp;&nbsp;&nbsp;Elt.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</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>
<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">12</td>
<td class="tdl_ws1 br">Mg</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"> </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">13</td>
<td class="tdl_ws1 br">Al</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">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>
<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">15</td>
<td class="tdl_ws1 br">P</td>
<td class="tdc br">2</td>
<td class="tdc">4</td>
<td class="tdc br">4</td>
<td class="tdc">4</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">16</td>
<td class="tdl_ws1 br">S</td>
<td class="tdc br">2</td>
<td class="tdc">4</td>
<td class="tdc br">4</td>
<td class="tdc">4</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>
<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">17</td>
<td class="tdl_ws1 br">Cl</td>
<td class="tdc br">2</td>
<td class="tdc">4</td>
<td class="tdc br">4</td>
<td class="tdc">4</td>
<td class="tdc">3</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">18</td>
<td class="tdl_ws1 br">A</td>
<td class="tdc br">2</td>
<td class="tdc">4</td>
<td class="tdc br">4</td>
<td class="tdc">4</td>
<td class="tdc">4</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">19</td>
<td class="tdl_ws1 br">K</td>
<td class="tdc br">2</td>
<td class="tdc">4</td>
<td class="tdc br">4</td>
<td class="tdc">4</td>
<td class="tdc">4</td>
<td class="tdc br">-</td>
<td class="tdc">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"> </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">20</td>
<td class="tdl_ws1 br">Ca</td>
<td class="tdc br">2</td>
<td class="tdc">4</td>
<td class="tdc br">4</td>
<td class="tdc">4</td>
<td class="tdc">4</td>
<td class="tdc br">-</td>
<td class="tdc">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"> </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">21</td>
<td class="tdl_ws1 br">Sc</td>
<td class="tdc br">2</td>
<td class="tdc">4</td>
<td class="tdc br">4</td>
<td class="tdc">4</td>
<td class="tdc">4</td>
<td class="tdc br">1</td>
<td class="tdc">(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"> </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">22</td>
<td class="tdl_ws1 br">Ti</td>
<td class="tdc br">2</td>
<td class="tdc">4</td>
<td class="tdc br">4</td>
<td class="tdc">4</td>
<td class="tdc">4</td>
<td class="tdc br">2</td>
<td class="tdc">(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"> </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"></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">29</td>
<td class="tdl_ws1 br">Cu</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">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"> </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">30</td>
<td class="tdl_ws1 br">Zn</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">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"> </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">31</td>
<td class="tdl_ws1 br">Ga</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">2</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"> </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">32</td>
<td class="tdl_ws1 br">Ge</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">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"> </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">33</td>
<td class="tdl_ws1 br">As</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">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"> </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">34</td>
<td class="tdl_ws1 br">Se</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">4</td>
<td class="tdc">2</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"></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">36</td>
<td class="tdl_ws1 br">Kr</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">4</td>
<td class="tdc">3</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">37</td>
<td class="tdl_ws1 br">Rb</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">4</td>
<td class="tdc">4</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"> </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">38</td>
<td class="tdl_ws1 br">Sr</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">4</td>
<td class="tdc">4</td>
<td class="tdc">-</td>
<td class="tdc br">-</td>
<td class="tdc">2</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">39</td>
<td class="tdl_ws1 br">Y</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">4</td>
<td class="tdc">4</td>
<td class="tdc">1</td>
<td class="tdc br">-</td>
<td class="tdc">(2)</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">40</td>
<td class="tdl_ws1 br">Zr</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">4</td>
<td class="tdc">4</td>
<td class="tdc">2</td>
<td class="tdc br">-</td>
<td class="tdc">(2)</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"><span class="pagenum" id="Page_10">[Pg 10]</span></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">47</td>
<td class="tdl_ws1 br">Ag</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">6</td>
<td class="tdc">6</td>
<td class="tdc">6</td>
<td class="tdc br">-</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>
<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">48</td>
<td class="tdl_ws1 br">Cd</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">6</td>
<td class="tdc">6</td>
<td class="tdc">6</td>
<td class="tdc br">-</td>
<td class="tdc">2</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">49</td>
<td class="tdl_ws1 br">In</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">6</td>
<td class="tdc">6</td>
<td class="tdc">6</td>
<td class="tdc br">-</td>
<td class="tdc">2</td>
<td class="tdc">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"> </td>
<td class="tdc"> </td>
<td class="tdc br"> </td>
<td class="tdc"> </td>
<td class="tdc"> </td>
</tr><tr>
<td class="tdl br">50</td>
<td class="tdl_ws1 br">Sn</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">6</td>
<td class="tdc">6</td>
<td class="tdc">6</td>
<td class="tdc br">-</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>
<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">51</td>
<td class="tdl_ws1 br">Sb</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">6</td>
<td class="tdc">6</td>
<td class="tdc">6</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 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">52</td>
<td class="tdl_ws1 br">Te</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">6</td>
<td class="tdc">6</td>
<td class="tdc">6</td>
<td class="tdc br">-</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"> </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">53</td>
<td class="tdl_ws1 br">I</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">6</td>
<td class="tdc">6</td>
<td class="tdc">6</td>
<td class="tdc br">-</td>
<td class="tdc">4</td>
<td class="tdc">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"> </td>
<td class="tdc"> </td>
<td class="tdc br"> </td>
<td class="tdc"> </td>
<td class="tdc"> </td>
</tr><tr>
<td class="tdl br">54</td>
<td class="tdl_ws1 br">Xe</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">6</td>
<td class="tdc">6</td>
<td class="tdc">6</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 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">55</td>
<td class="tdl_ws1 br">Cs</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">6</td>
<td class="tdc">6</td>
<td class="tdc">6</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 br">-</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 br"> </td>
<td class="tdc"> </td>
<td class="tdc"> </td>
</tr><tr>
<td class="tdl br">56</td>
<td class="tdl_ws1 br">Ba</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">6</td>
<td class="tdc">6</td>
<td class="tdc">6</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 br">-</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 br"> </td>
<td class="tdc"> </td>
<td class="tdc"> </td>
</tr><tr>
<td class="tdl br">57</td>
<td class="tdl_ws1 br">La</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">6</td>
<td class="tdc">6</td>
<td class="tdc">6</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 br">-</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 br"> </td>
<td class="tdc"> </td>
<td class="tdc"> </td>
</tr><tr>
<td class="tdl br">58</td>
<td class="tdl_ws1 br">Ce</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">6</td>
<td class="tdc">6</td>
<td class="tdc">6</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 br">-</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 br"> </td>
<td class="tdc"> </td>
<td class="tdc"> </td>
</tr><tr>
<td class="tdl br">59</td>
<td class="tdl_ws1 br">Pr</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">6</td>
<td class="tdc">6</td>
<td class="tdc">6</td>
<td class="tdc br">2</td>
<td class="tdc">4</td>
<td class="tdc">4</td>
<td class="tdc">3</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"> </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">71</td>
<td class="tdl_ws1 br">Lu</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">4</td>
<td class="tdc">4</td>
<td class="tdc">1</td>
<td class="tdc">-</td>
<td class="tdc br">-</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 br"> </td>
<td class="tdc"> </td>
<td class="tdc"> </td>
</tr><tr>
<td class="tdl br">72</td>
<td class="tdl_ws1 br">Hf</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">4</td>
<td class="tdc">4</td>
<td class="tdc">2</td>
<td class="tdc">-</td>
<td class="tdc br">-</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 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">79</td>
<td class="tdl_ws1 br">Au</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">1</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">80</td>
<td class="tdl_ws1 br">Hg</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">2</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">81</td>
<td class="tdl_ws1 br">Ti</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">2</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">82</td>
<td class="tdl_ws1 br">Pb</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"></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">83</td>
<td class="tdl_ws1 br">Bi</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">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&nbsp;&nbsp;&nbsp;<br>
Number&nbsp;&nbsp;&nbsp;</th>
<th class="tdc bb bt2 br" rowspan="2">&nbsp;&nbsp;&nbsp;Element&nbsp;&nbsp;&nbsp;</th>
<th class="tdc bb bt2 br" colspan="3">Ionization potential</th>
<th class="tdc bb bt2" rowspan="2">&nbsp;&nbsp;&nbsp;Reference&nbsp;&nbsp;&nbsp;</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&nbsp;&nbsp;&nbsp;</td>
<td class="tdl br">&nbsp;&nbsp;&nbsp;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">&nbsp;&nbsp;&nbsp;<a href="#1">1</a>, <a href="#2">2</a>, <a href="#3">3</a></td>
</tr><tr>
<td class="tdr br">2&nbsp;&nbsp;&nbsp;</td>
<td class="tdl br">&nbsp;&nbsp;&nbsp;He</td>
<td class="tdl br">25.4</td>
<td class="tdc br">24.47</td>
<td class="tdc br"> </td>
<td class="tdl">&nbsp;&nbsp;&nbsp;<a href="#5">5</a>, <a href="#4">4</a></td>
</tr><tr>
<td class="tdr br"></td>
<td class="tdl br">&nbsp;&nbsp;&nbsp;He+</td>
<td class="tdl br">54.3</td>
<td class="tdc br">54.18</td>
<td class="tdc br"> </td>
<td class="tdl">&nbsp;&nbsp;&nbsp;<a href="#3">3</a>, <a href="#5">5</a></td>
</tr><tr>
<td class="tdr br">3&nbsp;&nbsp;&nbsp;</td>
<td class="tdl br">&nbsp;&nbsp;&nbsp;Li</td>
<td class="tdl br"> </td>
<td class="tdc br">5.37</td>
<td class="tdc br"> </td>
<td class="tdl">&nbsp;&nbsp;&nbsp;<a href="#3">3</a></td>
</tr><tr>
<td class="tdr br"></td>
<td class="tdl br">&nbsp;&nbsp;&nbsp;Li+</td>
<td class="tdl br">40</td>
<td class="tdc br"></td>
<td class="tdc br"> </td>
<td class="tdl">&nbsp;&nbsp;&nbsp;<a href="#6">6</a></td>
</tr><tr>
<td class="tdr br">4&nbsp;&nbsp;&nbsp;</td>
<td class="tdl br">&nbsp;&nbsp;&nbsp;Be</td>
<td class="tdl br"> </td>
<td class="tdc br">9.6</td>
<td class="tdc br"> </td>
<td class="tdl">&nbsp;&nbsp;&nbsp;<a href="#7">7</a></td>
</tr><tr>
<td class="tdr br">5&nbsp;&nbsp;&nbsp;</td>
<td class="tdl br">&nbsp;&nbsp;&nbsp;B</td>
<td class="tdl br"> </td>
<td class="tdc br">8.3</td>
<td class="tdc br"> </td>
<td class="tdl">&nbsp;&nbsp;&nbsp;<a href="#7">7</a></td>
</tr><tr>
<td class="tdr br"> </td>
<td class="tdl br">&nbsp;&nbsp;&nbsp;B+</td>
<td class="tdl br"> </td>
<td class="tdc br">19.0</td>
<td class="tdc br"> </td>
<td class="tdl">&nbsp;&nbsp;&nbsp;<a href="#7">7</a></td>
</tr><tr>
<td class="tdr br">6&nbsp;&nbsp;&nbsp;</td>
<td class="tdl br">&nbsp;&nbsp;&nbsp;C+</td>
<td class="tdl br"> </td>
<td class="tdc br">24.3</td>
<td class="tdc br"> </td>
<td class="tdl">&nbsp;&nbsp;&nbsp;<a href="#8">8</a></td>
</tr><tr>
<td class="tdr br"> </td>
<td class="tdl br">&nbsp;&nbsp;&nbsp;C++</td>
<td class="tdl br"> </td>
<td class="tdc br"> </td>
<td class="tdc br">45</td>
<td class="tdl">&nbsp;&nbsp;&nbsp;<a href="#9">9</a>, <a href="#12">12</a></td>
</tr><tr>
<td class="tdr br">7&nbsp;&nbsp;&nbsp;</td>
<td class="tdl br">&nbsp;&nbsp;&nbsp;N</td>
<td class="tdl br">16.9</td>
<td class="tdc br"></td>
<td class="tdc br"> </td>
<td class="tdl">&nbsp;&nbsp;&nbsp;<a href="#10">10</a></td>
</tr><tr>
<td class="tdr br"> </td>
<td class="tdl br">&nbsp;&nbsp;&nbsp;N+</td>
<td class="tdl br"></td>
<td class="tdc br"></td>
<td class="tdc br">24</td>
<td class="tdl">&nbsp;&nbsp;&nbsp;<a href="#9">9</a>, <a href="#12">12</a></td>
</tr><tr>
<td class="tdr br"> </td>
<td class="tdl br">&nbsp;&nbsp;&nbsp;N++</td>
<td class="tdl br"></td>
<td class="tdc br"></td>
<td class="tdc br">45</td>
<td class="tdl">&nbsp;&nbsp;&nbsp;<a href="#9">9</a>, <a href="#12">12</a></td>
</tr><tr>
<td class="tdr br">8&nbsp;&nbsp;&nbsp;</td>
<td class="tdl br">&nbsp;&nbsp;&nbsp;O</td>
<td class="tdl br">15.5</td>
<td class="tdc br">13.56</td>
<td class="tdc br"> </td>
<td class="tdl">&nbsp;&nbsp;&nbsp;<a href="#3">3</a>, <a href="#11">11</a></td>
</tr><tr>
<td class="tdr br"> </td>
<td class="tdl br">&nbsp;&nbsp;&nbsp;O+</td>
<td class="tdl br"></td>
<td class="tdc br"></td>
<td class="tdc br">32</td>
<td class="tdl">&nbsp;&nbsp;&nbsp;<a href="#9">9</a>, <a href="#12">12</a></td>
</tr><tr>
<td class="tdr br"> </td>
<td class="tdl br">&nbsp;&nbsp;&nbsp;O++</td>
<td class="tdl br">50</td>
<td class="tdc br"></td>
<td class="tdc br">45</td>
<td class="tdl">&nbsp;&nbsp;&nbsp;<a href="#12">12</a></td>
</tr><tr>
<td class="tdr br">10&nbsp;&nbsp;&nbsp;</td>
<td class="tdl br">&nbsp;&nbsp;&nbsp;Ne</td>
<td class="tdl br">16.7</td>
<td class="tdc br"></td>
<td class="tdc br"> </td>
<td class="tdl">&nbsp;&nbsp;&nbsp;<a href="#13">13</a></td>
</tr><tr>
<td class="tdr br">11&nbsp;&nbsp;&nbsp;</td>
<td class="tdl br">&nbsp;&nbsp;&nbsp;Na</td>
<td class="tdl br">5.13</td>
<td class="tdc br">5.12</td>
<td class="tdc br"> </td>
<td class="tdl">&nbsp;&nbsp;&nbsp;<a href="#14">14</a>, <a href="#3">3</a></td>
</tr><tr>
<td class="tdr br"> </td>
<td class="tdl br">&nbsp;&nbsp;&nbsp;Na+</td>
<td class="tdl br">30-35</td>
<td class="tdc br"> </td>
<td class="tdc br"> </td>
<td class="tdl">&nbsp;&nbsp;&nbsp;<a href="#15">15</a></td>
</tr><tr>
<td class="tdr br">12&nbsp;&nbsp;&nbsp;</td>
<td class="tdl br">&nbsp;&nbsp;&nbsp;Mg</td>
<td class="tdl br">7.75</td>
<td class="tdc br">7.61</td>
<td class="tdc br"> </td>
<td class="tdl">&nbsp;&nbsp;&nbsp;<a href="#16">16</a>, <a href="#3">3</a></td>
</tr><tr>
<td class="tdr br"> </td>
<td class="tdl br">&nbsp;&nbsp;&nbsp;Mg+</td>
<td class="tdl br"> </td>
<td class="tdc br">14.97</td>
<td class="tdc br"> </td>
<td class="tdl">&nbsp;&nbsp;&nbsp;<a href="#3">3</a></td>
</tr><tr>
<td class="tdr br">13&nbsp;&nbsp;&nbsp;</td>
<td class="tdl br">&nbsp;&nbsp;&nbsp;Al</td>
<td class="tdl br"> </td>
<td class="tdc br">5.96</td>
<td class="tdc br"> </td>
<td class="tdl">&nbsp;&nbsp;&nbsp;<a href="#3">3</a></td>
</tr><tr>
<td class="tdr br"> </td>
<td class="tdl br">&nbsp;&nbsp;&nbsp;Al+</td>
<td class="tdl br"> </td>
<td class="tdc br">18.18</td>
<td class="tdc br"> </td>
<td class="tdl">&nbsp;&nbsp;&nbsp;<a href="#17">17</a></td>
</tr><tr>
<td class="tdr br"></td>
<td class="tdl br">&nbsp;&nbsp;&nbsp;Al++</td>
<td class="tdl br"> </td>
<td class="tdc br">28.32</td>
<td class="tdc br"> </td>
<td class="tdl">&nbsp;&nbsp;&nbsp;<a href="#17">17</a></td>
</tr><tr>
<td class="tdr br">14&nbsp;&nbsp;&nbsp;</td>
<td class="tdl br">&nbsp;&nbsp;&nbsp;Si</td>
<td class="tdl br"> </td>
<td class="tdc br">10.6</td>
<td class="tdc br">8.5</td>
<td class="tdl">&nbsp;&nbsp;&nbsp;<a href="#18">18</a>, <a href="#19">19</a></td>
</tr><tr>
<td class="tdr br"></td>
<td class="tdl br">&nbsp;&nbsp;&nbsp;Si+</td>
<td class="tdl br"> </td>
<td class="tdc br">16.27</td>
<td class="tdc br"></td>
<td class="tdl">&nbsp;&nbsp;&nbsp;<a href="#18">18</a></td>
</tr><tr>
<td class="tdr br"> </td>
<td class="tdl br">&nbsp;&nbsp;&nbsp;Si++</td>
<td class="tdl br"> </td>
<td class="tdc br"></td>
<td class="tdc br">31.66</td>
<td class="tdl">&nbsp;&nbsp;&nbsp;<a href="#18">18</a></td>
</tr><tr>
<td class="tdr br"></td>
<td class="tdl br">&nbsp;&nbsp;&nbsp;Si+++</td>
<td class="tdl br"> </td>
<td class="tdc br">44.95</td>
<td class="tdc br">8.5</td>
<td class="tdl">&nbsp;&nbsp;&nbsp;<a href="#18">18</a></td>
</tr><tr>
<td class="tdr br">15&nbsp;&nbsp;&nbsp;</td>
<td class="tdl br">&nbsp;&nbsp;&nbsp;P</td>
<td class="tdl br">13.3, 10.3</td>
<td class="tdc br"> </td>
<td class="tdc br"> </td>
<td class="tdl">&nbsp;&nbsp;&nbsp;<a href="#20">20</a>, <a href="#21">21</a></td>
</tr><tr>
<td class="tdr br"> </td>
<td class="tdl br">&nbsp;&nbsp;&nbsp;P++</td>
<td class="tdl br"> </td>
<td class="tdc br">29.8</td>
<td class="tdc br"></td>
<td class="tdl">&nbsp;&nbsp;&nbsp;<a href="#7">7</a></td>
</tr><tr>
<td class="tdr br"></td>
<td class="tdl br">&nbsp;&nbsp;&nbsp;P+++</td>
<td class="tdl br"> </td>
<td class="tdc br">45.3</td>
<td class="tdc br"></td>
<td class="tdl">&nbsp;&nbsp;&nbsp;<a href="#7">7</a></td>
</tr><tr>
<td class="tdr br">16&nbsp;&nbsp;&nbsp;</td>
<td class="tdl br">&nbsp;&nbsp;&nbsp;S</td>
<td class="tdl br">12.2</td>
<td class="tdc br">10.31</td>
<td class="tdc br"> </td>
<td class="tdl">&nbsp;&nbsp;&nbsp;<a href="#20">20</a>, <a href="#12">12</a></td>
</tr><tr>
<td class="tdr br"> </td>
<td class="tdl br">&nbsp;&nbsp;&nbsp;S+</td>
<td class="tdl br"> </td>
<td class="tdc br"></td>
<td class="tdc br">20</td>
<td class="tdl">&nbsp;&nbsp;&nbsp;<a href="#9">9</a>, <a href="#12">12</a></td>
</tr><tr>
<td class="tdr br"> </td>
<td class="tdl br">&nbsp;&nbsp;&nbsp;S++</td>
<td class="tdl br"></td>
<td class="tdc br"> </td>
<td class="tdc br">32</td>
<td class="tdl">&nbsp;&nbsp;&nbsp;<a href="#9">9</a>, <a href="#12">12</a></td>
</tr><tr>
<td class="tdr br"> </td>
<td class="tdl br">&nbsp;&nbsp;&nbsp;S+++</td>
<td class="tdl br"> </td>
<td class="tdc br">46.8</td>
<td class="tdc br"> </td>
<td class="tdl">&nbsp;&nbsp;&nbsp;<a href="#7">7</a></td>
</tr><tr>
<td class="tdr br">17&nbsp;&nbsp;&nbsp;</td>
<td class="tdl br">&nbsp;&nbsp;&nbsp;Cl</td>
<td class="tdl br">8.2</td>
<td class="tdc br"> </td>
<td class="tdc br"> </td>
<td class="tdl">&nbsp;&nbsp;&nbsp;<a href="#13">13</a></td>
</tr><tr>
<td class="tdr br">18&nbsp;&nbsp;&nbsp;</td>
<td class="tdl br">&nbsp;&nbsp;&nbsp;A</td>
<td class="tdl br">15.1</td>
<td class="tdc br"> </td>
<td class="tdc br"> </td>
<td class="tdl">&nbsp;&nbsp;&nbsp;<a href="#22">22</a></td>
</tr><tr>
<td class="tdr br"></td>
<td class="tdl br">&nbsp;&nbsp;&nbsp;A+</td>
<td class="tdl br">33, 34, 41.5</td>
<td class="tdc br"> </td>
<td class="tdc br"> </td>
<td class="tdl">&nbsp;&nbsp;&nbsp;<a href="#23">23</a>, <a href="#22">22</a>, <a href="#24">24</a></td>
</tr><tr>
<td class="tdr br">19&nbsp;&nbsp;&nbsp;</td>
<td class="tdl br">&nbsp;&nbsp;&nbsp;K</td>
<td class="tdl br">4.1</td>
<td class="tdc br">4.32</td>
<td class="tdc br"> </td>
<td class="tdl">&nbsp;&nbsp;&nbsp;<a href="#14">14</a>, <a href="#3">3</a></td>
</tr><tr>
<td class="tdr br"></td>
<td class="tdl br">&nbsp;&nbsp;&nbsp;K+</td>
<td class="tdl br">20-23</td>
<td class="tdc br"></td>
<td class="tdc br"> </td>
<td class="tdl">&nbsp;&nbsp;&nbsp;<a href="#14">14</a></td>
</tr><tr>
<td class="tdr br">20&nbsp;&nbsp;&nbsp;</td>
<td class="tdl br">&nbsp;&nbsp;&nbsp;Ca</td>
<td class="tdl br"></td>
<td class="tdc br">6.09</td>
<td class="tdc br"> </td>
<td class="tdl">&nbsp;&nbsp;&nbsp;<a href="#3">3</a></td>
</tr><tr>
<td class="tdr br"></td>
<td class="tdl br">&nbsp;&nbsp;&nbsp;Ca+</td>
<td class="tdl br"></td>
<td class="tdc br">11.82</td>
<td class="tdc br"> </td>
<td class="tdl">&nbsp;&nbsp;&nbsp;<a href="#3">3</a></td>
</tr><tr>
<td class="tdr br">21&nbsp;&nbsp;&nbsp;</td>
<td class="tdl br">&nbsp;&nbsp;&nbsp;Sc</td>
<td class="tdl br"></td>
<td class="tdc br"></td>
<td class="tdc br">6-9</td>
<td class="tdl">&nbsp;&nbsp;&nbsp;<a href="#25">25</a></td>
</tr><tr>
<td class="tdr br"></td>
<td class="tdl br">&nbsp;&nbsp;&nbsp;Sc+</td>
<td class="tdl br"></td>
<td class="tdc br"></td>
<td class="tdc br">12.5</td>
<td class="tdl">&nbsp;&nbsp;&nbsp;<a href="#19">19</a></td>
</tr><tr>
<td class="tdr br">22&nbsp;&nbsp;&nbsp;</td>
<td class="tdl br">&nbsp;&nbsp;&nbsp;Ti</td>
<td class="tdl br"></td>
<td class="tdc br">6.5</td>
<td class="tdc br"></td>
<td class="tdl">&nbsp;&nbsp;&nbsp;<a href="#26">26</a></td>
</tr><tr>
<td class="tdr br"></td>
<td class="tdl br">&nbsp;&nbsp;&nbsp;Ti+</td>
<td class="tdl br"></td>
<td class="tdc br"></td>
<td class="tdc br">12.5</td>
<td class="tdl">&nbsp;&nbsp;&nbsp;<a href="#19">19</a></td>
</tr><tr>
<td class="tdr br">23&nbsp;&nbsp;&nbsp;</td>
<td class="tdl br">&nbsp;&nbsp;&nbsp;V</td>
<td class="tdl br"></td>
<td class="tdc br"></td>
<td class="tdc br">6-9</td>
<td class="tdl">&nbsp;&nbsp;&nbsp;<a href="#25">25</a></td>
</tr><tr>
<td class="tdr br">24&nbsp;&nbsp;&nbsp;</td>
<td class="tdl br">&nbsp;&nbsp;&nbsp;Cr</td>
<td class="tdl br"></td>
<td class="tdc br">6.7</td>
<td class="tdc br"> </td>
<td class="tdl">&nbsp;&nbsp;&nbsp;<a href="#3">3</a></td>
</tr><tr>
<td class="tdr br">25&nbsp;&nbsp;&nbsp;</td>
<td class="tdl br">&nbsp;&nbsp;&nbsp;Mn</td>
<td class="tdl br"></td>
<td class="tdc br">7.41</td>
<td class="tdc br"> </td>
<td class="tdl">&nbsp;&nbsp;&nbsp;<a href="#35">35</a></td>
</tr><tr>
<td class="tdr br">26&nbsp;&nbsp;&nbsp;</td>
<td class="tdl br">&nbsp;&nbsp;&nbsp;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">&nbsp;&nbsp;&nbsp;<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">&nbsp;&nbsp;&nbsp;Fe</td>
<td class="tdl br"></td>
<td class="tdc br"></td>
<td class="tdc br">13</td>
<td class="tdl">&nbsp;&nbsp;&nbsp;<a href="#19">19</a></td>
</tr><tr>
<td class="tdr br">27&nbsp;&nbsp;&nbsp;</td>
<td class="tdl br">&nbsp;&nbsp;&nbsp;Co</td>
<td class="tdl br"></td>
<td class="tdc br"></td>
<td class="tdc br">6-9</td>
<td class="tdl">&nbsp;&nbsp;&nbsp;<a href="#25">25</a></td>
</tr><tr>
<td class="tdr br">28&nbsp;&nbsp;&nbsp;</td>
<td class="tdl br">&nbsp;&nbsp;&nbsp;Ni</td>
<td class="tdl br"></td>
<td class="tdc br"></td>
<td class="tdc br">6-9</td>
<td class="tdl">&nbsp;&nbsp;&nbsp;<a href="#25">25</a></td>
</tr><tr>
<td class="tdr br">29&nbsp;&nbsp;&nbsp;</td>
<td class="tdl br">&nbsp;&nbsp;&nbsp;Cu</td>
<td class="tdl br"></td>
<td class="tdc br">7.69</td>
<td class="tdc br"></td>
<td class="tdl">&nbsp;&nbsp;&nbsp;<a href="#3">3</a></td>
</tr><tr>
<td class="tdr br">30&nbsp;&nbsp;&nbsp;</td>
<td class="tdl br">&nbsp;&nbsp;&nbsp;Zn</td>
<td class="tdl br"></td>
<td class="tdc br">9.35</td>
<td class="tdc br"></td>
<td class="tdl">&nbsp;&nbsp;&nbsp;<a href="#3">3</a></td>
</tr><tr>
<td class="tdr br"></td>
<td class="tdl br">&nbsp;&nbsp;&nbsp;Zn+</td>
<td class="tdl br"></td>
<td class="tdc br">19.59</td>
<td class="tdc br"></td>
<td class="tdl">&nbsp;&nbsp;&nbsp;<a href="#7">7</a></td>
</tr><tr>
<td class="tdr br">31&nbsp;&nbsp;&nbsp;</td>
<td class="tdl br">&nbsp;&nbsp;&nbsp;Ga</td>
<td class="tdl br"></td>
<td class="tdc br">5.97</td>
<td class="tdc br"></td>
<td class="tdl">&nbsp;&nbsp;&nbsp;<a href="#3">3</a></td>
</tr><tr>
<td class="tdr br">33&nbsp;&nbsp;&nbsp;</td>
<td class="tdl br">&nbsp;&nbsp;&nbsp;As</td>
<td class="tdl br">11.5</td>
<td class="tdc br"> </td>
<td class="tdc br"></td>
<td class="tdl">&nbsp;&nbsp;&nbsp;<a href="#30">30</a></td>
</tr><tr>
<td class="tdr br">34&nbsp;&nbsp;&nbsp;</td>
<td class="tdl br">&nbsp;&nbsp;&nbsp;Se</td>
<td class="tdl br">12-13, 11.7</td>
<td class="tdc br"> </td>
<td class="tdc br"></td>
<td class="tdl">&nbsp;&nbsp;&nbsp;<a href="#31">31</a>, <a href="#32">32</a></td>
</tr><tr>
<td class="tdr br">35&nbsp;&nbsp;&nbsp;</td>
<td class="tdl br">&nbsp;&nbsp;&nbsp;Br</td>
<td class="tdl br">1.00</td>
<td class="tdc br"> </td>
<td class="tdc br"></td>
<td class="tdl">&nbsp;&nbsp;&nbsp;<a href="#13">13</a></td>
</tr><tr>
<td class="tdr br">36&nbsp;&nbsp;&nbsp;</td>
<td class="tdl br">&nbsp;&nbsp;&nbsp;Kr</td>
<td class="tdl br">14.5</td>
<td class="tdc br"> </td>
<td class="tdc br"></td>
<td class="tdl">&nbsp;&nbsp;&nbsp;<a href="#33">33</a></td>
</tr><tr>
<td class="tdr br">37&nbsp;&nbsp;&nbsp;</td>
<td class="tdl br">&nbsp;&nbsp;&nbsp;Rb</td>
<td class="tdl br">4.1</td>
<td class="tdc br">4.16</td>
<td class="tdc br"></td>
<td class="tdl">&nbsp;&nbsp;&nbsp;<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&nbsp;&nbsp;&nbsp;</td>
<td class="tdl br">&nbsp;&nbsp;&nbsp;Sr</td>
<td class="tdl br"></td>
<td class="tdc br">5.67</td>
<td class="tdc br"></td>
<td class="tdl">&nbsp;&nbsp;&nbsp;<a href="#3">3</a></td>
</tr><tr>
<td class="tdr br"></td>
<td class="tdl br">&nbsp;&nbsp;&nbsp;Sr+</td>
<td class="tdl br"></td>
<td class="tdc br">10.98</td>
<td class="tdc br"></td>
<td class="tdl">&nbsp;&nbsp;&nbsp;<a href="#3">3</a></td>
</tr><tr>
<td class="tdr br">42&nbsp;&nbsp;&nbsp;</td>
<td class="tdl br">&nbsp;&nbsp;&nbsp;Mo</td>
<td class="tdl br"></td>
<td class="tdc br">7.1, 7.35</td>
<td class="tdc br"></td>
<td class="tdl">&nbsp;&nbsp;&nbsp;<a href="#35">35</a>, <a href="#36">36</a></td>
</tr><tr>
<td class="tdr br">47&nbsp;&nbsp;&nbsp;</td>
<td class="tdl br">&nbsp;&nbsp;&nbsp;Ag</td>
<td class="tdl br"></td>
<td class="tdc br">7.54</td>
<td class="tdc br"></td>
<td class="tdl">&nbsp;&nbsp;&nbsp;<a href="#3">3</a></td>
</tr><tr>
<td class="tdr br">48&nbsp;&nbsp;&nbsp;</td>
<td class="tdl br">&nbsp;&nbsp;&nbsp;Cd</td>
<td class="tdl br"></td>
<td class="tdc br">8.95</td>
<td class="tdc br"></td>
<td class="tdl">&nbsp;&nbsp;&nbsp;<a href="#3">3</a></td>
</tr><tr>
<td class="tdr br"></td>
<td class="tdl br">&nbsp;&nbsp;&nbsp;Cd+</td>
<td class="tdl br"></td>
<td class="tdc br">18.48</td>
<td class="tdc br"></td>
<td class="tdl">&nbsp;&nbsp;&nbsp;<a href="#7">7</a></td>
</tr><tr>
<td class="tdr br">49&nbsp;&nbsp;&nbsp;</td>
<td class="tdl br">&nbsp;&nbsp;&nbsp;In</td>
<td class="tdl br"></td>
<td class="tdc br">5.75</td>
<td class="tdc br"></td>
<td class="tdl">&nbsp;&nbsp;&nbsp;<a href="#37">37</a></td>
</tr><tr>
<td class="tdr br">51&nbsp;&nbsp;&nbsp;</td>
<td class="tdl br">&nbsp;&nbsp;&nbsp;Sb</td>
<td class="tdl br">8.5 ± 1.0</td>
<td class="tdc br"></td>
<td class="tdc br"></td>
<td class="tdl">&nbsp;&nbsp;&nbsp;<a href="#26">26</a></td>
</tr><tr>
<td class="tdr br">53&nbsp;&nbsp;&nbsp;</td>
<td class="tdl br">&nbsp;&nbsp;&nbsp;I</td>
<td class="tdl br">10.1, 8.0</td>
<td class="tdc br"></td>
<td class="tdc br"></td>
<td class="tdl">&nbsp;&nbsp;&nbsp;<a href="#38">38</a>, <a href="#39">39</a></td>
</tr><tr>
<td class="tdr br">56&nbsp;&nbsp;&nbsp;</td>
<td class="tdl br">&nbsp;&nbsp;&nbsp;Ba</td>
<td class="tdl br"></td>
<td class="tdc br">5.19</td>
<td class="tdc br"></td>
<td class="tdl">&nbsp;&nbsp;&nbsp;<a href="#3">3</a></td>
</tr><tr>
<td class="tdr br"></td>
<td class="tdl br">&nbsp;&nbsp;&nbsp;Ba+</td>
<td class="tdl br"></td>
<td class="tdc br">9.96</td>
<td class="tdc br"></td>
<td class="tdl">&nbsp;&nbsp;&nbsp;<a href="#3">3</a></td>
</tr><tr>
<td class="tdr br">80&nbsp;&nbsp;&nbsp;</td>
<td class="tdl br">&nbsp;&nbsp;&nbsp;Hg</td>
<td class="tdl br"></td>
<td class="tdc br">10.4</td>
<td class="tdc br"></td>
<td class="tdl">&nbsp;&nbsp;&nbsp;<a href="#40">40</a></td>
</tr><tr>
<td class="tdr br">81&nbsp;&nbsp;&nbsp;</td>
<td class="tdl br">&nbsp;&nbsp;&nbsp;Tl</td>
<td class="tdl br"></td>
<td class="tdc br">6.94</td>
<td class="tdc br"></td>
<td class="tdl">&nbsp;&nbsp;&nbsp;<a href="#41">41</a></td>
</tr><tr>
<td class="tdr br">82&nbsp;&nbsp;&nbsp;</td>
<td class="tdl br">&nbsp;&nbsp;&nbsp;Pb</td>
<td class="tdl br">7.93</td>
<td class="tdc br">7.38</td>
<td class="tdc br"></td>
<td class="tdl">&nbsp;&nbsp;&nbsp;<a href="#42">42</a></td>
</tr><tr>
<td class="tdr br">83&nbsp;&nbsp;&nbsp;</td>
<td class="tdl br">&nbsp;&nbsp;&nbsp;Bi</td>
<td class="tdl br">8.0</td>
<td class="tdc br"></td>
<td class="tdc br"></td>
<td class="tdl">&nbsp;&nbsp;&nbsp;<a href="#30">30</a></td>
</tr><tr>
<td class="tdr bb br"></td>
<td class="tdl bb br">&nbsp;&nbsp;&nbsp;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">&nbsp;&nbsp;&nbsp;<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&nbsp;&nbsp;&nbsp;&nbsp;</th>
<th class="tdc">Reference</th>
<th class="tdc">Element&nbsp;&nbsp;&nbsp;&nbsp;</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&nbsp;&nbsp;</th>
<th class="tdc">Wilsing&nbsp;&nbsp;</th>
<th class="tdc">Rosenberg</th>
<th class="tdc_ws1_sa1">E.S. King<br>
Color Temperature&nbsp;&nbsp;</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&nbsp;</td>
<td class="tdc">18000&nbsp;</td>
<td class="tdc">15200&nbsp;</td>
<td class="tdc">14900&nbsp;</td>
     </tr><tr>
<td class="tdl">\(A_0\)</td>
<td class="tdc">10250&nbsp;</td>
<td class="tdc">&nbsp;1200</td>
<td class="tdc">11600&nbsp;</td>
<td class="tdc">11300&nbsp;</td>
   </tr><tr>
<td class="tdl">\(A_5\)</td>
<td class="tdc">&nbsp;&nbsp;9000</td>
<td class="tdc">&nbsp;&nbsp;9000</td>
<td class="tdc">&nbsp;&nbsp;8800</td>
<td class="tdc">&nbsp;&nbsp;8600</td>
   </tr><tr>
<td class="tdl">\(F_0\)</td>
<td class="tdc">&nbsp;&nbsp;7950</td>
<td class="tdc">&nbsp;&nbsp;7850</td>
<td class="tdc">&nbsp;&nbsp;7900</td>
<td class="tdc">&nbsp;&nbsp;7700</td>
   </tr><tr>
<td class="tdl">\(F_5\)</td>
<td class="tdc">&nbsp;&nbsp;6880</td>
<td class="tdc">&nbsp;&nbsp;6930</td>
<td class="tdc">&nbsp;&nbsp;7000</td>
<td class="tdc">&nbsp;&nbsp;6800</td>
   </tr><tr>
<td class="tdl">\(G_0\)</td>
<td class="tdc">&nbsp;&nbsp;5980</td>
<td class="tdc">&nbsp;&nbsp;6000</td>
<td class="tdc">&nbsp;&nbsp;6040</td>
<td class="tdc">&nbsp;&nbsp;5870</td>
   </tr><tr>
<td class="tdl">\(G_5\)</td>
<td class="tdc">&nbsp;&nbsp;5250</td>
<td class="tdc">&nbsp;&nbsp;5200</td>
<td class="tdc">&nbsp;&nbsp;5090</td>
<td class="tdc">&nbsp;&nbsp;4950</td>
   </tr><tr>
<td class="tdl">\(K_0\)</td>
<td class="tdc">&nbsp;&nbsp;4570</td>
<td class="tdc">&nbsp;&nbsp;4570</td>
<td class="tdc">&nbsp;&nbsp;4570</td>
<td class="tdc">&nbsp;&nbsp;4440</td>
   </tr><tr>
<td class="tdl">\(K_5\)</td>
<td class="tdc">&nbsp;&nbsp;3860</td>
<td class="tdc">&nbsp;&nbsp;3840</td>
<td class="tdc">&nbsp;&nbsp;3640</td>
<td class="tdc">&nbsp;&nbsp;3550</td>
   </tr><tr>
<td class="tdl">\(M_a\)</td>
<td class="tdc">&nbsp;&nbsp;3550</td>
<td class="tdc">&nbsp;&nbsp;3580</td>
<td class="tdc">&nbsp;&nbsp;3430</td>
<td class="tdc">&nbsp;&nbsp;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&nbsp;&nbsp;</th>
<th class="tdc_ws1_sa1">Coblentz<br>
Thermoelectric</th>
<th class="tdc_ws1_sa1">Plaskett<br>
Wedge Method&nbsp;&nbsp;</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&nbsp;</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&nbsp;</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&nbsp;</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&nbsp;</td>
<td class="tdc">&nbsp;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">&nbsp;9000</td>
<td class="tdc">&nbsp;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">&nbsp;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">&nbsp;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">&nbsp;6000</td>
<td class="tdc"></td>
<td class="tdc">&nbsp;8300</td>
   </tr><tr>
<td class="tdl">\(\alpha\)</td>
<td class="tdc">Aur(\(G_0\))</td>
<td class="tdc">&nbsp;5800</td>
<td class="tdc">&nbsp;6000</td>
<td class="tdc">5500-6000</td>
<td class="tdc">&nbsp;&nbsp;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">&nbsp;4000</td>
<td class="tdc"></td>
<td class="tdc">&nbsp;4200</td>
   </tr><tr>
<td class="tdl">\(\beta\)</td>
<td class="tdc">Gem(\(K_0\))</td>
<td class="tdc"></td>
<td class="tdc">&nbsp;5500</td>
<td class="tdc">5000-5500</td>
<td class="tdc">&nbsp;4200</td>
   </tr><tr>
<td class="tdl">\(\alpha\)</td>
<td class="tdc">Tau(\(K_5\))</td>
<td class="tdc">&nbsp;3000</td>
<td class="tdc">&nbsp;3500</td>
<td class="tdc"></td>
<td class="tdc">&nbsp;3400</td>
   </tr><tr>
<td class="tdl">\(\alpha\)</td>
<td class="tdc">Ori(\(M_a\))</td>
<td class="tdc">&nbsp;2600</td>
<td class="tdc">&nbsp;3000</td>
<td class="tdc"></td>
<td class="tdc">&nbsp;3400</td>
   </tr><tr>
<td class="tdl">\(\beta\)</td>
<td class="tdc">Peg(\(M_b\))</td>
<td class="tdc">&nbsp;2850</td>
<td class="tdc"></td>
<td class="tdc"></td>
<td class="tdc">&nbsp;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&nbsp;&nbsp;&nbsp;</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&nbsp;</td>
<td class="tdc">5770&nbsp;</td>
</tr><tr>
<td class="tdc">\(G_5\)</td>
<td class="tdc">4610&nbsp;</td>
<td class="tdc">5500&nbsp;</td>
</tr><tr>
<td class="tdc">\(K_0\)</td>
<td class="tdc">3860&nbsp;</td>
<td class="tdc">4880&nbsp;</td>
</tr><tr>
<td class="tdc">\(K_5\)</td>
<td class="tdc">3270&nbsp;</td>
<td class="tdc">4120&nbsp;</td>
</tr><tr>
<td class="tdc">\(M_a\)</td>
<td class="tdc">3080&nbsp;</td>
<td class="tdc">3330&nbsp;</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&nbsp;</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&nbsp;</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&nbsp;</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&nbsp;</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&nbsp;</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&nbsp;</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&nbsp;</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&nbsp;</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&nbsp;</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&nbsp;</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&nbsp;</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&nbsp;</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&nbsp;</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&nbsp;</td>
<td class="tdc">5580&nbsp;</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&nbsp;</td>
<td class="tdc">5440&nbsp;</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&nbsp;</td>
<td class="tdc">5530&nbsp;</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&nbsp;</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&nbsp;</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&nbsp;</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&nbsp;</td>
<td class="tdc">5300&nbsp;</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&nbsp;</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&nbsp;</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&nbsp;</td>
<td class="tdc">4840&nbsp;</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&nbsp;</td>
<td class="tdc">4700&nbsp;</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&nbsp;</td>
<td class="tdc">4790&nbsp;</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&nbsp;</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&nbsp;</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&nbsp;</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&nbsp;</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&nbsp;</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&nbsp;</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&nbsp;</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&nbsp;</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&nbsp;</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&nbsp;</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&nbsp;</td>
<td class="tdc">\(A_0\)</td>
<td class="tdc">10000&nbsp;&nbsp;</td>
     </tr><tr>
<td class="tdc">\(K_2\)</td>
<td class="tdc">3500&nbsp;</td>
<td class="tdc">\(B_8\)</td>
<td class="tdc">13500&nbsp;&nbsp;</td>
   </tr><tr>
<td class="tdc">\(K_0\)</td>
<td class="tdc">4000&nbsp;</td>
<td class="tdc">\(B_5\)</td>
<td class="tdc">15000&nbsp;&nbsp;</td>
   </tr><tr>
<td class="tdc">\(G_5\)</td>
<td class="tdc">5000&nbsp;</td>
<td class="tdc">\(B_3\)</td>
<td class="tdc">17000&nbsp;&nbsp;</td>
   </tr><tr>
<td class="tdc">\(G_0\)</td>
<td class="tdc">5600&nbsp;</td>
<td class="tdc">\(B_{1.5}\)</td>
<td class="tdc">18000&nbsp;&nbsp;</td>
   </tr><tr>
<td class="tdc">\(F_5\)</td>
<td class="tdc">7000&nbsp;</td>
<td class="tdc">\(B_0\)</td>
<td class="tdc">20000&nbsp;&nbsp;</td>
   </tr><tr>
<td class="tdc">\(F_0\)</td>
<td class="tdc">7500&nbsp;</td>
<td class="tdc">\(O\)</td>
<td class="tdc">25000&nbsp;&nbsp;</td>
   </tr><tr>
<td class="tdc">\(A_5\)</td>
<td class="tdc">8400&nbsp;</td>
<td class="tdc"></td>
<td class="tdc">35000&nbsp;&nbsp;</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">&nbsp;&nbsp;Class&nbsp;&nbsp;</th>
<th class="tdc bb bt2 br" colspan="2">&nbsp;&nbsp;Mean density&nbsp;&nbsp;</th>
<th class="tdc bb bt2 br" colspan="2">&nbsp;&nbsp;Radius&nbsp;&nbsp;</th>
<th class="tdc bb bt2" colspan="2">&nbsp;&nbsp;Product&nbsp;&nbsp;</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">&nbsp;&nbsp;4.6</td>
<td class="tdl br">&nbsp;&nbsp;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">&nbsp;&nbsp;1.2</td>
<td class="tdl br">&nbsp;&nbsp;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">&nbsp;&nbsp;0.9</td>
<td class="tdl br">&nbsp;&nbsp;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">&nbsp;&nbsp;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">\(r\)&nbsp;&nbsp;</th>
<th class="tdc">&nbsp;&nbsp;\(d\)&nbsp;&nbsp;</th>
<th class="tdc">&nbsp;&nbsp;\(T\)&nbsp;&nbsp;</th>
<th class="tdc">&nbsp;&nbsp;\(r\)&nbsp;&nbsp;</th>
<th class="tdc">&nbsp;&nbsp;\(d\)&nbsp;&nbsp;</th>
<th class="tdc">&nbsp;&nbsp;\(T\)</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&nbsp;</td>
<td class="tdc">5</td>
<td class="tdl">0.00015</td>
<td class="tdr">730,000&nbsp;</td>
     </tr><tr>
<td class="tdc">2</td>
<td class="tdc">0.0215</td>
<td class="tdc">3,840,000&nbsp;</td>
<td class="tdc">6</td>
<td class="tdl">0.0000093</td>
<td class="tdr">290,000&nbsp;</td>
   </tr><tr>
<td class="tdc">3</td>
<td class="tdc">0.0050</td>
<td class="tdc">2,370,000&nbsp;</td>
<td class="tdc">6.9</td>
<td class="tdl">0.000000</td>
<td class="tdr">......&nbsp;&nbsp;&nbsp;&nbsp;</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&nbsp;&nbsp;</td>
<td class="tdl">&nbsp;&nbsp;less than \(10^{-1}\)</td>
   </tr><tr>
<td class="tdl">Line Sharpness&nbsp;&nbsp;</td>
<td class="tdl">&nbsp;&nbsp;less than \(10^{-1}\)</td>
     </tr><tr>
<td class="tdl">Line Width&nbsp;&nbsp;</td>
<td class="tdl">&nbsp;&nbsp;\(10^{-6}\)</td>
   </tr><tr>
<td class="tdl">Flash Spectrum&nbsp;&nbsp;</td>
<td class="tdl">&nbsp;&nbsp;\(2~\times~ 10^{-5}\)</td>
   </tr><tr>
<td class="tdl">Radiative Equilibrium&nbsp;&nbsp;</td>
<td class="tdl">&nbsp;&nbsp;order of \(10^{-4}\)</td>
   </tr><tr>
<td class="tdl">Limit of Balmer Series&nbsp;&nbsp;</td>
<td class="tdl">&nbsp;&nbsp;\(10^{-3}\) to \(10^{-4}\) (upper limit)</td>
   </tr><tr>
<td class="tdl">(Ionization&nbsp;&nbsp;</td>
<td class="tdl">&nbsp;&nbsp;\(10^{-4}\) 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">&nbsp;&nbsp;Int.&nbsp;&nbsp;</th>
<th class="tdc bb bt2 br">&nbsp;&nbsp;Cl.&nbsp;&nbsp;</th>
<th class="tdc bb bt2 br">Attribution</th>
<th class="tdc bb bt2 br">&nbsp;&nbsp;Int.&nbsp;&nbsp;</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">&nbsp;&nbsp;Int.&nbsp;&nbsp;</th>
<th class="tdc bb bt2 br">&nbsp;&nbsp;Cl.&nbsp;&nbsp;</th>
<th class="tdc bb bt2 br">Attribution</th>
<th class="tdc bb bt2 br">&nbsp;&nbsp;Int.&nbsp;&nbsp;</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">&nbsp;&nbsp;Int.&nbsp;&nbsp;</th>
<th class="tdc bb bt2 br">Attribution</th>
<th class="tdc bb bt2 br">&nbsp;&nbsp;Int.&nbsp;&nbsp;</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">&nbsp;&nbsp;Int.&nbsp;&nbsp;</th>
<th class="tdc bb bt2 br">&nbsp;&nbsp;Cl.&nbsp;&nbsp;</th>
<th class="tdc bb bt2 br">Attribution</th>
<th class="tdc bb bt2 br">&nbsp;&nbsp;Int.&nbsp;&nbsp;</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">&nbsp;&nbsp;Int.&nbsp;&nbsp;</th>
<th class="tdc bb bt2 br">Attribution</th>
<th class="tdc bb bt2 br">&nbsp;&nbsp;Int.&nbsp;&nbsp;</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">&nbsp;&nbsp;Int.&nbsp;&nbsp;</th>
<th class="tdc bb bt2 br">Attribution</th>
<th class="tdc bb bt2 br">&nbsp;&nbsp;Int.&nbsp;&nbsp;</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.&nbsp;&nbsp;</th>
<th class="tdc">Element&nbsp;&nbsp;</th>
<th class="tdc">Remark&nbsp;&nbsp;</th>
<th class="tdc">At. No.&nbsp;&nbsp;</th>
<th class="tdc">Element&nbsp;&nbsp;</th>
<th class="tdc">&nbsp;&nbsp;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&nbsp;&nbsp;</th>
<th class="tdc_ws1 bb bt2 br">Ionization<br>
Potential&nbsp;&nbsp;</th>
<th class="tdc bb bt2 br">Wave-lenght&nbsp;&nbsp;</th>
<th class="tdc_ws1 bb bt2">&nbsp;&nbsp;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">&nbsp;&nbsp;\(log~ n_r\)&nbsp;&nbsp;</th>
<th class="tdc bb bt2 br">&nbsp;&nbsp;Intensity&nbsp;&nbsp;</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">&nbsp;&nbsp;\(log~ n_r\)&nbsp;&nbsp;</th>
<th class="tdc bb bt2">&nbsp;&nbsp;Intensity&nbsp;&nbsp;</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&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</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&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</th>
<th class="tdc">Rowland&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</th>
<th class="tdc"></th>
<th class="tdc">Assigned&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</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&nbsp;&nbsp;</th>
<th class="tdc bb bt2">&nbsp;&nbsp;Int.&nbsp;&nbsp;</th>
<th class="tdc bb bt2 br">\(\sigma\)&nbsp;&nbsp;</th>
<th class="tdc bb bt2">Line&nbsp;&nbsp;</th>
<th class="tdc bb bt2">&nbsp;&nbsp;Int.&nbsp;&nbsp;</th>
<th class="tdc bb bt2 br">\(\sigma\)&nbsp;&nbsp;</th>
<th class="tdc bb bt2">Line&nbsp;&nbsp;</th>
<th class="tdc bb bt2">&nbsp;&nbsp;Int.&nbsp;&nbsp;</th>
<th class="tdc bb bt2 br">\(\sigma\)&nbsp;&nbsp;</th>
<th class="tdc bb bt2">Line&nbsp;&nbsp;</th>
<th class="tdc bb bt2">&nbsp;&nbsp;Int.&nbsp;&nbsp;</th>
<th class="tdc bb bt2 br">\(\sigma\)&nbsp;&nbsp;</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">&nbsp;&nbsp;Series&nbsp;&nbsp;</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&nbsp;&nbsp;</th>
<th class="tdc">&nbsp;&nbsp;Note&nbsp;&nbsp;</th>
<th class="tdl">&nbsp;&nbsp;&nbsp;Max.&nbsp;&nbsp;&nbsp;</th>
<th class="tdc">&nbsp;&nbsp;Blends&nbsp;&nbsp;</th>
<th class="tdc">&nbsp;&nbsp;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&nbsp;&nbsp;</th>
<th class="tdc_ws1 bb bt2 br">&nbsp;&nbsp;Ionization<br>
Potential&nbsp;&nbsp;</th>
<th class="tdc_ws1 bb bt2 br">&nbsp;&nbsp;Excitation<br>
Potential&nbsp;&nbsp;</th>
<th class="tdc bb bt2 br">&nbsp;&nbsp;Max.&nbsp;&nbsp;</th>
<th class="tdc bb bt2 br">&nbsp;&nbsp;\(T_{max}\)&nbsp;&nbsp;</th>
<th class="tdc bb bt2 br">\(log~ P_e\)</th>
<th class="tdc bb bt2 br">&nbsp;&nbsp;\(log~ n_r\)&nbsp;&nbsp;</th>
<th class="tdc bb bt2">&nbsp;&nbsp;Sum&nbsp;&nbsp;</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&nbsp;&nbsp;</th>
<th class="tdc_ws1 bb bt2 br">&nbsp;&nbsp;Ionization<br>
Potential&nbsp;&nbsp;</th>
<th class="tdc_ws1 bb bt2 br">&nbsp;&nbsp;Excitation<br>
Potential&nbsp;&nbsp;</th>
<th class="tdc bb bt2 br">&nbsp;&nbsp;Max.&nbsp;&nbsp;</th>
<th class="tdc bb bt2">&nbsp;&nbsp;\(T_{max}\)&nbsp;&nbsp;</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&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</th>
<th class="tdc">Temperature</th>
<th class="tdc">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</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&nbsp;</th>
<th class="tdc">&nbsp;&nbsp;&nbsp;Source&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</th>
<th class="tdc">&nbsp;&nbsp;&nbsp;Max.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</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&nbsp;</th>
<th class="tdc">&nbsp;&nbsp;&nbsp;Ionization Potential&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</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">&nbsp;&nbsp;Atom&nbsp;&nbsp;</th>
<th class="tdc bb bt2 br">&nbsp;&nbsp;Series&nbsp;&nbsp;</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">&nbsp;&nbsp;Atom&nbsp;&nbsp;</th>
<th class="tdc bb bt2">&nbsp;&nbsp;Series&nbsp;&nbsp;</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">&nbsp;&nbsp;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">&nbsp;&nbsp;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">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Series&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</th>
<th class="tdc bb bt2 br">&nbsp;&nbsp;Line&nbsp;&nbsp;</th>
<th class="tdc bb bt2 br" colspan="3">&nbsp;&nbsp;&nbsp;&nbsp;Classes&nbsp;&nbsp;&nbsp;&nbsp;</th>
<th class="tdc bb bt2 br" colspan="2">Atom</th>
<th class="tdc bb bt2 br">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Series&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</th>
<th class="tdc bb bt2 br">&nbsp;&nbsp;Line&nbsp;&nbsp;</th>
<th class="tdc bb bt2" colspan="3">&nbsp;&nbsp;&nbsp;&nbsp;Classes&nbsp;&nbsp;&nbsp;&nbsp;</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&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</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">&nbsp;&nbsp;&nbsp;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">&nbsp;&nbsp;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">&nbsp;&nbsp;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">&nbsp;&nbsp;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">&nbsp;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">&nbsp;&nbsp;Ca+*</td>
<td class="tdc"></td>
<td class="tdc_top">Ca</td>
<td class="tdc_top">&nbsp;&nbsp;Fe*</td>
<td class="tdc_top">&nbsp;&nbsp;Ti*</td>
<td class="tdc_top">&nbsp;&nbsp;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">&nbsp;&nbsp;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">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;}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">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;}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">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</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">\(k\)&nbsp;&nbsp;&nbsp;</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">&nbsp;&nbsp;Class&nbsp;&nbsp;</th>
<th class="tdc bb bt2 br" colspan="2">&nbsp;&nbsp;Star&nbsp;&nbsp;</th>
<th class="tdc bb bt2 br">&nbsp;&nbsp;Boss&nbsp;&nbsp;</th>
<th class="tdc bb bt2 br">&nbsp;&nbsp;m&nbsp;&nbsp;</th>
<th class="tdc bb bt2 br">&nbsp;&nbsp;H&nbsp;&nbsp;</th>
<th class="tdc bb bt2 br">&nbsp;&nbsp;Class&nbsp;&nbsp;</th>
<th class="tdc bb bt2 br" colspan="2">&nbsp;&nbsp;Star&nbsp;&nbsp;</th>
<th class="tdc bb bt2 br">&nbsp;&nbsp;Boss&nbsp;&nbsp;</th>
<th class="tdc bb bt2 br">&nbsp;&nbsp;m&nbsp;&nbsp;</th>
<th class="tdc bb bt2">&nbsp;&nbsp;H&nbsp;&nbsp;</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">&nbsp;&nbsp;Atom&nbsp;&nbsp;</th>
<th class="tdc bb bt2 br">&nbsp;&nbsp;Line&nbsp;&nbsp;</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&nbsp;&nbsp;</th>
<th class="tdc">Note&nbsp;&nbsp;</th>
<th class="tdl">Maximum&nbsp;&nbsp;</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">&nbsp;&nbsp;H. D.&nbsp;&nbsp;</th>
<th class="tdc bb bt2 br" colspan="2">&nbsp;&nbsp;Star&nbsp;&nbsp;</th>
<th class="tdc bb bt2 br">&nbsp;&nbsp;m&nbsp;&nbsp;</th>
<th class="tdc bb bt2 br">&nbsp;&nbsp;H&nbsp;&nbsp;</th>
<th class="tdc bb bt2 br">&nbsp;&nbsp;Class&nbsp;&nbsp;</th>
<th class="tdc bb bt2 br">&nbsp;&nbsp;Metalic<br>
Lines</th>
<th class="tdc bb bt2 br">&nbsp;&nbsp;Line<br>
Quality</th>
<th class="tdc bb bt2 br">&nbsp;&nbsp;H<br>
wings</th>
<th class="tdc bb bt2 br">&nbsp;&nbsp;Sr+&nbsp;&nbsp;</th>
<th class="tdc bb bt2">&nbsp;&nbsp;Si+&nbsp;&nbsp;</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;">&nbsp;</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;">&nbsp;</span>astrophysical <a href="#Page_156">156</a></li>
<li class="isub1"><span style="margin-left: 2em;">"</span><span style="margin-left: 2em;">&nbsp;</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>


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