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A cryogenic linear rf trap has been constructed to study the accuracy of a clock based on laser cooled /sup 199/Hg/sup +/. Crystals of tens of ions have been observed. The residual micromotion of the ions has been minimized and Ramsey interrogation periods of 100 s have been demonstrated for the 40.5 GHz transition. Systematic shifts to the clock transition due to magnetic field fluctuations as well as heating of the ions during the clock cycle have been evaluated. This system should eventually provide a frequency standard of high precision and accuracy.