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Travel times of PcP and P phases from nuclear and high explosive sources are interpreted in terms of variations in the radius of the earth's outer core. This interpretation favors a core which is slightly larger and has less ellipticity than the Taggart-Engdahl reference model. Other interpretations in terms of lateral variation in mantle velocity are possible. Because of the geographic distribution of events and stations, only the northern hemisphere of the core is represented. A modified spherical harmonic analysis method is used to smooth the data and to estimate the shape of the core. The variation of core radius determined from this representation of data truncated at one standard deviation is approximately plus or minus 10 kilometers on the basis of terms to degree and order 5. Variations in geoid height resulting from the inferred variations in core radius do not correlate with, but are of the same order of magnitude as, those determined from satellite observations. PcP amplitude/period shows little variation with ep central distance. The PcP phase is generally shorter in apparent period than the P phase. This relationship is reversed, however, for arrivals from the Novaya Zemlya event of October 27, 1966. Ray tracing techniques are used to estimate the perturbation of the PcP-P time interval and PcP/P amplitude ratio produced by a hypothetical upper mantle low velocity zone of varying thickness.