A focusing differential Cˇerenkov counter of high velocity resolution using a gas radiator has been developed and used in relativistic particle beams. The optical and mechanical features are described. The velocity &bgr; can be varied continuously from 0.81 to 1.00. These counters give a velocity resolution &Dgr;&bgr;/&bgr; of 0.0025 (half‐width at half‐maximum) at &bgr;=0.9985 and an average efficiency for a 4‐in. diameter particle aperture of 0.7 in a particle beam collimated to ±1°. The sources of spurious response and the ultimate limitations of counters of this type are discussed.