This paper discusses the principles of measuring radial velocities directly with a photoelectric spectrometer and describes an experimental instrument for use in such measurements. Possible sources of systematic error are discussed, and reasons are given for supposing them to be capable of producing errors only of the order of 0.1 km/sec. Observations of bright late-type stars confirm the freedom of the method from appreciable systematic errors. They demonstrate that the standard deviation of one photoelectric measurement of the velocity of a 5-mag star is about 1 km/sec, practically the same as that of an a-quality velocity in the General Catalogue of Stellar Radial Velocities. Using a 36-inch telescope, one can determine velocities of stars at least as faint as m = 9 at a rate of 6-8 per hour.