The Earth's lower mantle and outer core are identified by seismology as regions that are homogeneous in composition and mineral structure over wide pressure ranges. Variations with pressure, P, of bulk modulus, K, density, , and, for the lower mantle, rigidity modulus, , are reported in seismic models with much greater resolution than is achieved over similar pressure ranges by laboratory methods. These data are an under-utilized resource for high pressure equation-of-state studies. The lower mantle data are particularly useful for two reasons: (1) the minerals believed to be present can be obtained in metastable equilibrium at low pressure for laboratory examination, (2) a linear relationship between , K and P allows extrapolation to infinite pressure, giving a direct estimate of . The core equation-of-state is less well constrained, but two independent approaches give . Although not always recognized is a parameter of every equation-of-state, but none of the usual equations gives values compatible with terrestrial data. A new approach is proposed, representing as a function of , since at infinite pressure and the endpoint of the equation-of-state is precisely determined. Two equations that fit all of the observations are suggested. This use of is particularly relevant to estimates of thermodynamic properties at high pressure because it constrains the dimensionless derivatives and on which these estimates depend.