deletions | additions       diff --git a/Gradients.tex b/Gradients.tex  index 1b75714..25efaa0 100644  --- a/Gradients.tex  +++ b/Gradients.tex 
...
\Delta \T (\Delta r) = \T'(r + \Delta r) - \T(r + \delta r) \simeq \Delta r \bigg[ \frac{\D \T'}{\D r}-\frac{\D \T}{\D r}\bigg].  \end{equation}  Assuming $\T' \simeq \T$, i.e. the temperature is not changing drastically within the distance $\Delta r$, one can write   \begin{equation} \begin{equation}\label{eq:deltat}  \Delta \T (\Delta r) = \Delta r \, \T \bigg[ -\frac{\D \ln \T}{\D r}- \bigg(-\frac{\D \ln \T'}{\D r}\bigg)\bigg],  \end{equation}  and using the assumption of pressure equilibrium, the definitions of pressure scale height $\hp$ and the gradients $\nabla$ and $\nabla'$ we obtain