Using available sets of magnitude determinations, primarily from Uppsala seismological bulletin, various extensions are made of the Zurich magnitude recommendations of 1967. Thus, body-wave magnitude (m) and surface-wave magnitudes (M) are related to each other for 12 different earthquake regions as well as world-wide. Depth corrections for M are derived for all focal depths. Formulas are developed which permit calculation of M also from vertical component long-period seismographs. Body-wave magnitudes from broad-band and narrow-band short-period seismographs are compared and relations deduced. Applications are made both to underground nuclear explosions and to earthquakes. The possibilities of explosion-earthquake discrimination on the bas...