A new magnitude scale Mt is defined by using the logarithm of the maximum amplitude of far-field tsunami waves measured by tide gauges or their substitutes. The Mt scale is experimentally adjusted to the Mw scale introduced by Kanamori (1977), so that the Mt scale measures the seismic moment of a tsunamigenic earthquake as well as the overall size of tsunami at the source. Mt and the conventional tsunami magnitude m are distinct scales. By using many amplitude data of tsunami waves now available the values of Mt are assigned to 65 tsunamigenic earthquakes that occurred in the Pacific area during the period form 1837 to 1974. The 1960 Chilean shock has the largest Mt. 9.4. The 1946 Aleutian (Mt=9.3), the 1837 Chilean (Mt=91/4), and the 1964 Alaskan (Mt=9.1) events follow. Nine great events having Mt=9 or over occurred during this period, and their occurrence is clustered in the years around 1840, 1870, and 1960. Of all the 65 events listed, at least six unusual earthquakes having tsunamis with an amplitude disproportionately large for their surface-wave magnitude Ms are identified from the Mt-Ms relation.