More than 700 seismograms of 39 shocks recorded mainly in southern California at epicentral distances between 105 and 140 degrees are used to investigate records of phases which have penetrated the earth's core. Properties of PKIKP, SKP, SKIKP, PKS, and PKIKS are discussed. Portions of travel-time curves of these phases are revised. Travel times of waves starting and ending at the surface of the core, and wave velocities in the core, are recalculated. Between about 1,500 and 1,200 km. from the earth's center in the transition zone from the liquid outer to the probably solid inner core, waves having lengths of the order of 10 km. travel faster than longer waves. This is probably caused by a rather rapid increase in viscosity toward the earth's center in this transition zone.