Editing 3Dconfigurations/DescriptionOfRiemannTypeI (section)

===Extracted from Table 6a of XXVIII===

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<td align="center" colspan="12" bgcolor="lightgreen">
'''Data Extracted from Table 6a (p. 871) of <br />
{{ Chandrasekhar66_XXVIIIfigure }}
<br />&nbsp;<br />[&nbsp;Also appears as Table XIII(a) on p. 170 of [[Appendix/References#EFE|<font color="red">EFE</font>]] ]
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<td align="center" colspan="3" rowspan="2">Our<br /> (reverse-engineered)<br /> Determination<br />of Index Symbols</td>
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  <td align="center" colspan="12">''The Properties of Marginally Overstable Riemann Ellipsoids of Type I''</td>
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  <td align="center" rowspan="2"><math>\frac{a_2}{a_1}</math></td>
  <td align="center" rowspan="2"><math>\frac{a_3}{a_1}</math></td>
  <td align="center" rowspan="11" bgcolor="lightgrey" width="3%">&nbsp;</td>
  <td align="center" colspan="4">Direct</td>
  <td align="center" rowspan="11" bgcolor="lightgrey" width="3%">&nbsp;</td>
  <td align="center" colspan="4">Adjoint</td>
  <td align="center" rowspan="2" bgcolor="red"><font color="white">A<sub>1</sub></font></td>
  <td align="center" rowspan="2" bgcolor="red"><font color="white">A<sub>2</sub></font></td>
  <td align="center" rowspan="2" bgcolor="red"><font color="white">A<sub>3</sub></font></td>
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  <td align="center"><math>\Omega_2</math></td>
  <td align="center"><math>\Omega_3</math></td>
  <td align="center"><math>\zeta_2</math></td>
  <td align="center"><math>\zeta_3</math></td>

  <td align="center"><math>\Omega_2^\dagger</math></td>
  <td align="center"><math>\Omega_3^\dagger</math></td>
  <td align="center"><math>\zeta_2^\dagger</math></td>
  <td align="center"><math>\zeta_3^\dagger</math></td>
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  <td align="right" bgcolor="lightblue">1.0000</td>
  <td align="right" bgcolor="lightblue">0.3033</td>
  <td align="right" bgcolor="lightblue">&nbsp;0.0000</td>
  <td align="right" bgcolor="lightblue">+0.7073</td>
  <td align="right" bgcolor="lightblue">&nbsp;0.0000</td>
  <td align="right" bgcolor="lightblue">-2.7417</td>

  <td align="right" bgcolor="lightblue">&nbsp;0.0000</td>
  <td align="right" bgcolor="lightblue">+1.3708</td>
  <td align="right" bgcolor="lightblue">&nbsp;0.0000</td>
  <td align="right" bgcolor="lightblue">-1.4147</td>

  <td align="right" bgcolor="lightblue">0.341295655</td>
  <td align="right" bgcolor="lightblue">0.341295655</td>
  <td align="right" bgcolor="lightblue">1.317408690</td>
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  <td align="right">1.0526</td>
  <td align="right">0.3712</td>
  <td align="right">+0.1283</td>
  <td align="right">+0.7176</td>
  <td align="right">-1.5014</td>
  <td align="right">-2.5977</td>

  <td align="right">+0.4898</td>
  <td align="right">+1.2972</td>
  <td align="right">-0.3931</td>
  <td align="right">-1.4371</td>

  <td align="right">0.39892471</td>
  <td align="right">0.37240741</td>
  <td align="right">1.22866788</td>
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  <td align="right">1.1111</td>
  <td align="right">0.4230</td>
  <td align="right">+0.2153</td>
  <td align="right">+0.7098</td>
  <td align="right">-1.8984</td>
  <td align="right">-2.3978</td>

  <td align="right">+0.6812</td>
  <td align="right">+1.1922</td>
  <td align="right">-0.6000</td>
  <td align="right">-1.4275</td>

  <td align="right">0.44194613</td>
  <td align="right">0.38437206</td>
  <td align="right">1.17368182</td>
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  <td align="right">1.1765</td>
  <td align="right">0.4560</td>
  <td align="right">+0.2942</td>
  <td align="right">+0.6901</td>
  <td align="right">-2.1276</td>
  <td align="right">-2.1787</td>

  <td align="right">+0.8032</td>
  <td align="right">+1.0751</td>
  <td align="right">-0.7794</td>
  <td align="right">-1.3984</td>

  <td align="right">0.47156283</td>
  <td align="right">0.38075039</td>
  <td align="right">1.14768677</td>
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  <td align="right" bgcolor="yellow">1.2500</td>
  <td align="right" bgcolor="yellow">0.4703</td>
  <td align="right" bgcolor="yellow">+0.3639</td>
  <td align="right" bgcolor="yellow">+0.6633</td>
  <td align="right" bgcolor="yellow">-2.2794</td>
  <td align="right" bgcolor="yellow">-1.9637</td>

  <td align="right" bgcolor="yellow">+0.8778</td>
  <td align="right" bgcolor="yellow">+0.9579</td>
  <td align="right" bgcolor="yellow">-0.9450</td>
  <td align="right" bgcolor="yellow">-1.3599</td>

  <td align="right" bgcolor="yellow">0.48950275</td>
  <td align="right" bgcolor="yellow">0.36484494</td>
  <td align="right" bgcolor="yellow">1.14565231</td>
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  <td align="right">1.3333</td>
  <td align="right">0.4676</td>
  <td align="right">+0.4269</td>
  <td align="right">+0.6329</td>
  <td align="right">-2.3842</td>
  <td align="right">-1.7621</td>

  <td align="right">+0.9150</td>
  <td align="right">+0.8458</td>
  <td align="right">-1.1125</td>
  <td align="right">-1.3186</td>

  <td align="right">0.49697204</td>
  <td align="right">0.33963373</td>
  <td align="right">1.16339423</td>
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  <td align="right">1.4286</td>
  <td align="right">0.4474</td>
  <td align="right">+0.4877</td>
  <td align="right">+0.5999</td>
  <td align="right">-2.4626</td>
  <td align="right">-1.5752</td>

  <td align="right">+0.9178</td>
  <td align="right">+0.7400</td>
  <td align="right">-1.3082</td>
  <td align="right">-1.2768</td>

  <td align="right">0.49205257</td>
  <td align="right">0.30602987</td>
  <td align="right">1.20191756</td>
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  <td align="right">1.5385</td>
  <td align="right">0.4053</td>
  <td align="right">+0.5550</td>
  <td align="right">+0.5635</td>
  <td align="right">-2.5307</td>
  <td align="right">-1.3984</td>

  <td align="right">+0.8807</td>
  <td align="right">+0.6390</td>
  <td align="right">-1.5937</td>
  <td align="right">-1.2330</td>

  <td align="right">0.47004307</td>
  <td align="right">0.26291500</td>
  <td align="right">1.26704192</td>
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  <td align="right">1.6722</td>
  <td align="right">0.3278</td>
  <td align="right" bgcolor="pink">+0.7107</td>
  <td align="right" bgcolor="pink">+0.5142</td>
  <td align="right" bgcolor="pink">-2.4011</td>
  <td align="right" bgcolor="pink">-1.1673</td>

  <td align="right" bgcolor="pink">+0.7107</td>
  <td align="right" bgcolor="pink">+0.5142</td>
  <td align="right" bgcolor="pink">-2.4011</td>
  <td align="right" bgcolor="pink">-1.1673</td>

  <td align="right">0.42132864</td>
  <td align="right">0.19910085</td>
  <td align="right">1.37957051</td>
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  <td align="left" colspan="15">NOTE: &nbsp; All frequencies are given in the unit of <math>(\pi G \rho)^{1 / 2}</math>.  Also &hellip;
<ul><li>The model highlighted with a light-blue background is a Maclaurin spheroid; in this case we determined the values of the index symbols, <math>A_1</math>, <math>A_2</math>, and <math>A_3</math>, from the analytic expressions given in our [[Apps/MaclaurinSpheroids#Gravitational_Potential|accompanying discussion of the gravitational potential of oblate spheroids]].</li>  <li>The model highlighted with a yellow background is the example that we have used elsewhere in this MediaWiki chapter to illustrate the trajectories of Lagrangian fluid elements.</li> <li>The model whose frequencies have been highlighted with a pink background appears to be self-adjoint.</li></ul> </td>
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