Phase velocity as a function of period has been determined for Rayleigh waves in the period range 100 to 400 seconds. The results were derived from a study of seismograms from the southeastern Alaska earthquake of July 10, 1958, and from published data on the Assam earthquake of August 15, 1950. The method depends on measurement of the travel time of wave crests along an arc of known length, with proper correction for change of period with distance. For observations of a single Rayleigh wave train at a single pair of observing stations, crest identification is uncertain, and so too is the resulting curve of phase velocity versus period. A set of phase velocity curves may be computed, each one corresponding to a different choice of crest identification. Only one of these is consistent with the data from several earthquakes and several pairs of observing stations. In the present work, high precision in phase velocity measurement is achieved by using the observations of the Rayleigh waves R3 and R5 at Pasadena of the Assam earthquake. Data from the southeastern Alaska earthquake are used to resolve the ambiguity resulting from uncertainty in crest identification. The final phase velocity curve is estimated to be accurate to better than one per cent in the range of periods 100 to 400 seconds.