Seismic waves produced by explosions near Soltau were observed at distances up to 50 km., and others from the Heligoland explosion from 50 to 1000 km. Special time signals and a high recording speed enabled the instant of a sharp onset to be determined to 0 \cdot 1 sec. Short-range seismic data were used to eliminate some of the effect of rocks near the surface. The average velocity of the first arrivals was 4 \cdot 4 km./sec. between 4 and 24 km. from the shot point, 5 \cdot 95 km./sec. between 24 and 120 km., and 8 \cdot 18 km./sec. beyond 120 km. Significant local variations were found at the shorter distances. Alternative hypotheses covering the distribution of velocity in the upper layers gave estimates of 27 \cdot 4 and 29 \cdot 6 km. for the depth of the ultrabasic layer. Later arrivals proved difficult to identify, and a statistical method was used to estimate the significance of travel-time curves drawn through selected groups of onsets. This test showed that P * was not significantly recorded, but a number of onsets at 7 or 8 sec. after Pn probably represented a wave travelling for most of its path in the ultrabasic layer and reflected at the critical angle between that layer and the surface. The test failed to decide whether the onsets close to the expected times of P g should be treated as one or more phases. Confused motion persisted during the period when transverse waves were expected, but, with the possible exception of S n, there was no significant concentration of observations about lines representing recognized phases. The thermal energy of the Heligoland explosion was 1 \cdot 3 × 1020 ergs, and the energy in the seismic waves was of the order of 1017 ergs. The efficiency was therefore comparable with that of a surface explosion, and measurements of the crater confirmed that the rock which covered the charge could not have had much effect on the momentum entering the ground.