Editing SSC/PerspectiveReconciliation (section)

==Step 1:==
Following Rosseland, we adopt as a supplemental relation what we have [[SR/IdealGas#Consequential_Ideal_Gas_Relations|referred to elsewhere]] as,

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<span id="ConservingMass:Lagrangian"><font color="#770000">'''Form B'''</font></span><br />
of the Ideal Gas Equation of State,

{{Math/EQ_EOSideal02}}
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where, for our purposes, we assume that {{Math/MP_AdiabaticIndex}} is independent of space and time.  Plugging the function, <math>~\epsilon(P,\rho)</math>, that is defined by this equation of state into the adiabatic form of the 1<sup>st</sup> law of thermodynamics leads to the relations (see, respectively, Rosseland's equations 2.8 and 2.9),
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<math>~\frac{dP}{dt}</math>
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<math>~=</math>
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<math>~\frac{\gamma_g P}{\rho} \frac{d\rho}{dt} \, ,</math>
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and,
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<math>~\frac{P}{P_0} </math>
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<math>~=</math>
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<math>~\biggl( \frac{\rho}{\rho_0}\biggr)^{\gamma_g} \, ,</math>
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where <math>~P_0</math> and <math>~\rho_0</math> are independent of time.  We note for later use that, when the equation of continuity &#8212; as written in its original vector-operator form &#8212; is combined with this last differential form of the 1<sup>st</sup> law of thermodynamics, we can write,
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<math>~\frac{dP}{dt}</math>
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<math>~=</math>
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<math>~- \gamma_g P \nabla\cdot \vec{v} \, .</math>
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