deletions | additions       diff --git a/The_stellar_clusters_are_well__.tex b/The_stellar_clusters_are_well__.tex  index 4319f5b..59a36e3 100644  --- a/The_stellar_clusters_are_well__.tex  +++ b/The_stellar_clusters_are_well__.tex 
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\begin{equation}  V^2 = \frac{2 G M_d}{R_d} y^2 [I_0(y)K_0(y)-I_1(y)K_1(y)]  \end{equation}  where $y\equiv R/(2R_d)$, $M_d$, the disk mass, is $6.4\times 10^{10}~M_{\odot}$ and $R_d$, the scale length, is 2.9 kpc. For this curve, the epicyclic frequency is   \begin{equation}  \varkappa^2 = \frac{4 G M_d}{R_d^3} \left\{ \left[2 I_0(y)+yI_1(y)\right]K_0(y)-\left[y I_0(y)+I_1(y)\right]K_1(y)\right\}  \end{equation}