Sound velocities determined in iron, shock compressed to pressures between 77 GPa and 400 GPa, indicate that two phase transitions exist on the Hugoniot. A discontinuity in sound velocities at 200¿2 GPa may mark the transition of ϵ iron to &ggr; iron. A second discontinuity at 243¿2 GPa is believed to indicate the onset of melting. The calculated temperature at melting lies between 5000 K and 5700 K. When extrapolated from the Hugoniot melting point, the Lindermann criterion yields an estimate of 5800¿500 K for the melting of pure iron at the inner core boundary pressure of 330 GPa. The product of density times the thermodynamic Gr¿neisen parameter in liquid iron, calculated from the present data, is 19.6¿0.8 Mg m-3. A temperature profile ranging from 3800 K at the core-mantle boundary to 5000 K at the earth's center is calculated using the present data. Sound velocities for ϵ iron provide a better match to seismic velocities for the earth's inner core than do those of &ggr; iron. A comparison between liquid iron velocities and the velocity profile through the outer core provides further evidence for alloying of iron with ''lighter elements'' in the core.