With the presumption that a shifted Maxwellian velocity distribution adequately describes the electrons in a flowing plasma, the details of a method to measure their directed velocity are described. The system consists of a ruby laser source and two detectors set 180° from each other and both set at 90° with respect to the incident laser beam. The lowest velocity that can be determined by this method depends on the electron thermal velocity. The application of this diagnostic to the measurement of flow velocities in plasma being lost from the ends of 9-pinch devices is described.