Abstract In the bulletin of the Harvard Seismograph Station, under date of September 15, 1935, attention was directed to the unusual character of certain records from the vicinity of 17° N, 62° W. One of the novel features was a short-period phase about 23 minutes after P. It has become known as T, for third, with P and S constituting the first and second groups of short-period waves of similar general appearance. The problem was discussed with Weston, and since that time those two stations have been working on it. Linehan published in 1940 the first description outside station bulletins. From detailed studies of more than 250 earthquakes, with all records from Harvard and Weston and selected ones from Fordham, Ottawa, and Tucson, the following results have been obtained. The T phase ranges in period from 0.5 to 1.0 sec. It originates under the ocean and is characteristic of oceanic areas. It is generated by earthquakes of which the majority are between about 40 and 100 km. in depth. It clearly is not limited to shallow foci. It has been observed at Harvard and Weston from distances between 1,060 and 7,000 km.; from foci north of the Greater Antilles, near Bermuda, on the Mid-Atlantic Ridge in the North Atlantic, and south of the equator; originating under water ranging down to 3,000 fathoms in depth. It consists primarily of shear waves, with a velocity of between 1.6 and 2.7 km/sec. over oceanic paths and 2.1 km/sec. over land. (The velocity of sound in water of the Atlantic Ocean is from 1.46 to 1.53 km/sec.). It is suggested that the T phase may be short-period shear waves traveling in ocean-bottom sediments and the top continental layer. An overwhelming preponderance of the evidence contradicts any hypothesis that significant amounts of the energy are water-borne. A progressively changing angle of approach for waves in different parts of the T phase has been observed at Harvard and Weston. In 1949, the Columbia University group composed of Ewing, Press, and Tolstoy, under a government contract, printed two reports on this subject, “The T phase of Shallow-Focus Submarine Earthquakes,” and “Proposed Tsunami Warning System.” The former was based largely on 20 Weston records which were included without discussion of the investigation or its results with either Weston or Harvard. They decided that “the T phase is characterized by periods of 0.5 sec. or less, a velocity identical with that of sound in water for the part of its path crossing deep water and by speeds from 12,000 to 18,000 ft/sec. (3.7 to 5.5 km/sec.) across shallow water or land,” and that “propagation through the sound channel accounts for the major part of the observed T phase.” In checking their report against the original Weston records, we find that they have made elementary errors, such as misreading iP from −16 to +18 sec., and incorrectly computing epicentral distance by more than a degree. These and many others so greatly affect the fundamental solution of the problem that their conclusions cannot be accepted. This aspect will be discussed in a separate paper.