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\def\kms{$\rm {km}~\rm s^{-1}$}
We have obtained 100--600 stellar velocities in each of the central regions of the globular clusters M15, 47~Tuc, N6397, and M30. These clusters are known to have either a centrally-concentrated surface brightness profile or an inner cusp. To alleviate the severe crowding problems in these clusters, we have used an imaging Fabry-Perot Interferometer which is the most efficient instrument for measuring velocities in these dense regions (see Gebhardt et al. 1994, AJ, submitted). Combining our data with published velocities for stars in the outer parts of the cluster allows us to determine the projected velocity dispersion profile with an accuracy of a few \kms\ for most of the radial extent of the clusters.
Using a previously measured surface brightness profile and our velocity dispersion profile, we estimate the mass distribution of the cluster by inverting the Jeans equation under the assumption of isotropy. This determines the mass density profile non-parametrically and provides strong constraints for the modelling of globular clusters. For M15, we find that the density profile between radii of 0.2\arcmin\ and 2.0\arcmin\ has a power law exponent of --2.4, which is close to the theoretical prediction for core-collapse clusters. In the clusters analysed so far, 47~Tuc and M15, we find a significant increase of the M/L$_{\mathrm V}$ in the central regions, indicating mass segregation. In M15, we measure an increase in the M/L$_{\mathrm V}$ from 2 at 0.8\arcmin\ to 6 at 0.5\arcmin.
