We present slitless spectra of 10 Seyfert galaxies observed with the Space Telescope Imaging Spectrograph on the Hubble Space Telescope. The spectra cover the [OIII] 4959, 5007 emission lines at a spectral resolving power of ~9000 and a spatial resolution of 0.1. We compare the slitless spectra with previous HST narrow-band images to determine the velocity shifts and dispersions of the bright emission-line knots in the narrow-line regions (NLRs) of these Seyferts. Many knots are spatially resolved with sizes of tenths of arcsecs, corresponding to tens of pcs, and yet they appear to move coherently with radial velocities between zero and +/- 1200 km/s with respect to the systemic velocities of their hostgalaxies. The knots also show a broad range in velocity dispersion, ranging from ~30 km/s (the velocity resolution) to ~1000 km/s FWHM. Most of the Seyfert galaxies in this sample show an organized flow pattern, with radial velocities near zero at the nucleus (defined by the optical continuum peak) and increasing to maximum blueshifts and redshifts within ~1 of the nucleus, followed by a decline to the systemic velocity. The emission-line knots also follow a general trend of decreasing velocity dispersion with increasing distance. In the Seyfert 2 galaxies, the presence of blueshifts and redshifts on either side of the nucleus indicates that rotation alone cannot explain the observed radial velocities, and that radial outflow plays an important role. Each of the Seyfert galaxies in this sample (with the exception of Mrk 3) shows a bright, compact (FWHM < 0.5) [O III] knot at the position of its optical nucleus. These nuclear emission-line knots have radial-velocity centroids near zero, but they typically have the highest velocity dispersions.
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