A nuclear magnetic resonance experiment which may be used to measure with high precision the average value of a magnetic field over an extended path in space is described. The nuclei, contained in a flowing liquid, are excited at one point and detected at another downstream from the point of excitation. Under proper conditions the average value of the magnetic field along the flow path between points of excitation and detection may be obtained therefrom. Some experimental criteria which must be met in order that this average be correctly obtained are discussed. The results of such an experiment are presented. Although the accuracy of the measurement may be somewhat less than this, line widths of 1 part in 107have been obtained.