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A description is given of a instrument that makes use of an iodine absorption cell, a coud\`e echelle spectrograph, and a sophisticated software analysis package to reduce relative radial velocity errors by two orders of magnitude. Short and long term errors have been reduced to 5 and 20 m/s respectively.
Using an iodine cell, radial velocity measurements are more sensitive to small amplitude stellar variations than photometric techniques. A survey is being made of stars previously thought to be stable that lie in or near the Cepheid instability strip. This survey has uncovered the smallest amplitude Cepheid yet known (HR 7796).
The iodine cell has been used to obtain radial velocity curves from several hundred optical absorption lines in four bright Cepheid variables. Differential velocities between various classes of lines reveal detail about velocity fields and shocks in the atmospheres of Cepheids and provide the raw information needed to construct detailed physical models. As a first order correction to the Barnes-Evans/Baade-Wesselink method, it is suggested that the amplitude of radial velocity curves be reduced by 10% to better match the motion of the optical continuum forming region. These observations reveal no unambiguous examples of line splitting. The shape and amplitude of the radial velocity curve of $\delta$ Cep is shown to have been extremely constant over most of the last century.
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