Editing SSC/FreeEnergy/EquilibriumSequenceInstabilities (section)

====Jeans (1919)====
From &sect; 51 (p. 47) of  [http://adsabs.harvard.edu/abs/1919pcsd.book.....J J. H. Jeans (1919)] &#8212; ''verbatum'' text in green:  <font color="green">
The simplest problem occurs when the secondary may be treated as a rigid sphere;  this is the special problem dealt with by Roche.  As in &sect; 47 the tide-generating potential acting on the primary may be supposed to be
</font>
<div align="center">
<table border="0" cellpadding="5" align="center">

<tr>
  <td align="left">
<math>~\frac{M^'}{R} + \frac{M^'}{R^2} x + \frac{M^'}{R^3}(x^2 - \tfrac{1}{2}y^2 - \tfrac{1}{2}z^2) + \cdots </math>
  </td>
</tr>
</table>
</div>
<font color="green">We shall for the present be content to omit all terms beyond those written down.  The correction required by the neglect of these terms will be discussed later, and will be found to be so small that the results now to be obtained are hardly affected.</font>

<font color="green">On omitting these terms, and combining the two potentials &hellip; it appears that the primary may be supposed influenced by a statical field of potential
</font>
<div align="center">
<table border="0" cellpadding="5" align="center">

<tr>
  <td align="left">
<math>~\frac{M^'}{R} x\biggr(1 - \frac{\omega^2 R^3}{M + M^'}\biggr) + \frac{M^'}{R^3}(x^2 - \tfrac{1}{2}y^2 - \tfrac{1}{2}z^2) 
+ \tfrac{1}{2}\omega^2(x^2 + y^2)       \, .</math>
  </td>
</tr>
</table>
</div>
<font color="green">The terms in <math>~x</math> may immediately be removed by supposing <math>~\omega</math> to have the appropriate value given by
</font>
<div align="center">
<table border="0" cellpadding="5" align="center">

<tr>
  <td align="right">
<math>~\omega^2</math>
  </td>
  <td align="center">
<math>~=</math>
  </td>
  <td align="left">
<math>~\frac{M+M^'}{R^3}</math>
  </td>
</tr>
</table>
</div>
<font color="green">and the condition for equilibrium is now seen to be that we shall have, at every point of the surface,
</font>
<div align="center">
<table border="0" cellpadding="5" align="center">

<tr>
  <td align="right">
<math>~V_b + \mu (x^2 - \tfrac{1}{2}y^2 - \tfrac{1}{2}z^2) + \tfrac{1}{2}\omega^2(x^2 + y^2)     </math>
  </td>
  <td align="center">
<math>~=</math>
  </td>
  <td align="left">
constant
  </td>
</tr>
</table>
</div>
<font color="green">where <math>~\mu</math> … stands for <math>~M^'/R^3</math> .
</font>