deletions | additions       diff --git a/Convective Velocities.tex b/Convective Velocities.tex  index cbf5df2..999af76 100644  --- a/Convective Velocities.tex  +++ b/Convective Velocities.tex 
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\frac{\D\rho}{\rho} = \alpha \frac{\D\P}{\P} - \delta \frac{\D T}{T} + \phi {\D\mu}{\mu}   \end{equation}  Where   $ \phi \equiv \big(\frac{\partial \ln \rho}{\partial \ln \mu} \big)_{\P,T}, \; \delta \equiv - \big(\frac{\partial \ln \rho}{\partial \ln T} \big)_{\P,\mu}, \; \alpha \equiv \big(\frac{\partial \ln \rho}{\partial \ln \P} \big)_{\mu,T}$ and for an ideal gas $\alpha = \delta = \phi = 1$ 1$, so that using pressure equilibrium ($\D\P= 0$) we obtain $\Delta \ln \rho = \Delta \ln T$.   In the case of a mixture of perfect gas and radiation we can write   \begin{equation}  \Delta \ln \rho = -Q \Delta \ln T  \end{equation}  where  \begin{equation}  Q = \frac{4-3 \beta}{\beta} - \bigg(\frac{\partial \ln \mu}{\partial \ln T} \bigg)_{\P},  \end{equation}  with $\beta = \P_{Gas}/\P$  write, assuming again pressure equilibr