Atmospheric refraction, with its non-predictable variations, is one of the dominant sources of error in the precise determination of the apparent position of a star. It appears that this will be the dominant error source for the new generation of instrumentation now being installed for the determination of stellar catalog and Universal Time (i.e., the USNO 65-cm PZT). The effects of anomalous refraction measurements of stellar position propagate to the various quantities derived from this data. This includes the compilation of stellar catalogs, the determination of Universal Time, and variations in the latitude.