The acoustic velocity, refractive index, and equation of state of liquid ammonia dihydrate under high pressure and high temperature J. Chem. Phys. 137, 104504 (2012) Ultrafast acoustics measurements on liquid mercury have been performed at high pressure and temperature in a diamond anvil cell using picosecond acoustic interferometry. We extract the density of mercury from adiabatic sound velocities using a numerical iterative procedure. We also report the pressure and temperature dependence of the thermal expansion, isothermal and adiabatic compressibility, bulk modulus, and pressure derivative of the latter up to 7 GPa and 520 K. We finally show that the sound velocity follows a scaling law as a function of density in the overall measured metallic state.