deletions | additions       diff --git a/Wave Propagation.tex b/Wave Propagation.tex  index ca0e6ff..f9899d4 100644  --- a/Wave Propagation.tex  +++ b/Wave Propagation.tex 
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\label{eqn:magnetodisp2}  k^2 \simeq \frac{N^2 k_\perp^2}{\omega^2}.  \end{equation}  Gravity waves have fluid velocity nearly perpendicular to the stratification (i.e., nearly horizontal). Their group velocity is primarily horizontal, with  \begin{equation}  \label{eqn:vgravperp}  v_{g,\perp} = \frac{\omega}{k_\perp} \, ,  \end{equation}  but with a small  radial component of $v_{g,r} \begin{equation}  \label{eqn:vgravr}  v_{g,r}  = \omega^2/(N k_\perp)$. k_\perp) \, .   \end{equation}  For non-negligible buoyancy or magnetic field, the slow and fast magneto-gravity waves have similar characteristics. In the limit of very strong magnetic field or stratification (such that the second term in the square root of equation \ref{eqn:magnetodisp} dominates), we have  \begin{equation}