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Four high-resolution (30,000) integrated-light echelle spectra were obtained in July 1993 in the core of the globular cluster M15, with the ESO/NTT Telescope and EMMI, at the European Southern Observatory, La Silla, Chile. Seeing values were $\simeq$ 0.9{$^{\prime\prime}$}. Each exposure, through a 1{$^{\prime\prime}$} x 8{$^{\prime\prime}$} slit, is displaced by 1{$^{\prime\prime}$} in order to sample a total area of 4{$^{\prime\prime}$} x 8{$^{\prime\prime}$}, which encompasses the area where Peterson {et\thinspace al.} (1989, ApJ, 347, 251) obtained velocity dispersion values 8.4 $\leq$ {$\sigma_p$} $\leq$ 30.0 {km\thinspace s$^{-1}$}. The unique imaging/spectroscopic capabilities of EMMI allow a very precise a priori/posteriori positioning of the slit. The data reduction by cross-correlation technique, taking advantage of the spatial resolution along the slit, provides radial velocities {V$_{r}$} and velocity dispersions {$\sigma_p$} at all locations in the 4{$^{\prime\prime}$} x 8{$^{\prime\prime}$} area. Most of our cross-correlation functions (CCFs) are dominated by the light from one or two bright stars, implying narrow or double CCFs, respectively, as predicted by our simulations (Dubath {et\thinspace al.}, 1994, ApJ, in press) which show that when the light in the sampling area is dominated by one star, the derived velocity dispersion is too small, and when the light is dominated by two stars with unusually large radial velocity differences, the derived velocity dispersion is too large. All our present {$\sigma_p$} values, derived from the Doppler line broadening of our CCFs, are always $\leq$ 17 {km\thinspace s$^{-1}$}, at any location in the 4{$^{\prime\prime}$} x 8{$^{\prime\prime}$} area. The velocity dispersion from the average of all normalized CCFs is {$\sigma_p$} = 11.9 {km\thinspace s$^{-1}$}. The radial velocities of the 11 best resolved (spatially or spectroscopically) bright stars are also determined; they give {$\sigma_p$} = 17.3 $\pm$ 3.7 {km\thinspace s$^{-1}$}. We have radial velocities for two of the three brightest stars (AC \# 214, 215, 216, Auri\`ere and Cordoni, 1981, A\&A, 100, 307) of the former unresolved cusp, the third being too blue to provide a {V$_{r}$} value. Two of the brightest stars, separated by 2.5{$^{\prime\prime}$}, AC \# 212 and 215, have radial velocity values differing by 48.9 {km\thinspace s$^{-1}$}. The integrated light spectrum with light contributions from these two stars gives a broadened CCF, with nevertheless {$\sigma_p$} $\simeq$ 15.2 {km\thinspace s$^{-1}$}. We do not find any evidence for a strong core velocity dispersion cusp (Dubath and Meylan, 1994, A\&A).
