In a recent article, Anderson has derived a relationship which relates the temperature dependence of the bulk modulus of a solid as a function of the specific heat and atomic volume as follows, dB s dT = -δ γ(C p V) , where all the symbols have the usual meanings with the exception of δ. The term δ, which is a fundamental parameter of a solid similar to the Grüneisen parameter γ, was recently introduced by Anderson. In the present paper, this term is referred to as the Anderson Grüneisen parameter which is equal to 1 α (d ln B 3 dT ) . This relationship between δ and α and d ln B 3 dT was originally derived by Grüneisen and more recently by Anderson based on the Mie-Grüneisen equation of state and Mie's formula to represent the potential energy of a solid. Using the recent thermal-elastic data of MgO, Anderson showed that the parameters is virtually independof temperature. In the present paper, an equation describing the temperature dependence of the bulk modulus of a solid is derived in a different manner using standard thermodynamic relationships based on the Grüneisen equation, α = γC v B T V . By comparing this equation with the equation derived by Anderson, it is shown immediately that the Anderson-Grüneisen parameter δ is related to the pressure dependence of the bulk modulus, i.e. δ = ( δB s dP ) − 1 . If one further assumes that the Poisson's ratios is independent of volume, this parameter 8 is related to the familiar Grüneisen parameter γ. Two equations relating 8 and y are derived, i.e. δ = 2γ − 2 3 and δ = 2 γ. The first equation between δ and γ is derived using the relationship between γ and dB s dP by Slater and the second using that by Dugdale and MacDonald. For MgO, the values of δ obtained are : δ=3·1 when δ = 1 α d ln B s dT δ=2·86 when δ= dB s dP −1 δ=2· 39 whenδ=2γ− 2 3 δ=3·06 when δ=2γ The calculated values of B s for MgO using the different values of δ agree well with the experimental data with the exception of δ = 2.39, for which the predicted bulk modulus values are somewhat too high.