We have reexamined the adiabatic and melting gradients in the core and the relationship between them. We consider possible contributions to CV and &ggr; in the core from vibrational, electronic, and magnetic (ferromagnetic and Schottky anomaly) terms. Both vibrational and electronic terms are important in the core. Magnetic terms are probably not important, but any contribution they make will tend to make &ggr; larger. Considering these contributions we find that 1.2<&ggr;<2.0 in the core. This evaluation of &ggr; is consistent with the idea of adiabatic circulation in the core and a reasonable extrapolation of the melting gradient of iron, using, for example, the Lindenmann--Gilvarry melting model. The Kraut--Kennedy melting mdel predicts a comparatively small melting point gradient under core conditions, prohibiting convection unless &ggr;<1.0. We find that the ''core paradox'' of Higgins and Kennedy has been somewhat exaggerated owing to numerical errors in calculating the adiabat.