Travel times of normal earthquakes are made the basis for calculated travel times for shocks at depths down to 800 km. These are presented in tabular form, together with certain auxiliary data. Theoretical discussion is given for the critical distances at which pP and PP, sP and SP, etc., coincide, and below which these phases should not occur. These distances are not focal points (caustics). Methods are given for determining epicenter, depth, and origin time, and are applied to a selected group of shocks. The results of different methods agree very well with one another and with the calculated travel-time data. A preliminary report is given on certain characteristics of the shocks studied. The mechanism of deep-focus earthquakes is discussed briefly, and it is concluded that normal and deep-focus earthquakes are probably brought about by the same forces.