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CCD ``scan" observing is a popular method for observing large regions of the sky in a rapid manner, and the ad hoc assumption is often made that the transit of a star across the chip can be well represented by uniform and rectilinear motion. Although this is a good assumption near the celestial equator, it fails at higher declinations and in a manner dependent on the scale of the telescope, the physical size of the CCD, and by the declination being observed. Standard astrometric reductional techniques are not appropriate in diurnal scan observing, since the projection of the sky onto the CCD is not spherical. Methods for reducing CCD scan data have been developed at the U.S. Naval Observatory at Flagstaff for high precision astrometry using numerical techniques to model the distortions inherent in scan observing and tested on the observatory's 20-cm transit telescope. Scan observations have been made of regions at declinations $\delta$ $\sim$ 0$^o$, 44$^o$, and 70$^o$ with accurately known star positions. With the corrections applied, there is very good agreement ($\sigma \sim \pm$0.1 arcsec) between these positions and those determined with the transit telescope. Without the corrections applied, the agreement is very poor for the higher declinations. This paper describes these techniques and predicts the sizes of these distortions, based on model results, for a wide range of telescope scales, CCD dimensions, and declinations being observed. \vfill\eject\bye
