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From thermodynamics and the Hugoniot jump relations I derive a simple algebraic equation among the Grüneisen constant γ , bulk modulus B s , pressure P, particle velocity U p , and slope s and intercept c of the tangent line to the U s − U p Hugoniot at U p . At U p = 0 , s is simply related to ∂B s / ∂P) s and for 10 km/ s< U p< 100 − 200 km/ s there is a very linear region in the U s − U p curve. When dP / dρ = ∞, s and the curvature are directly given by P, B s and γ . I end with thedoi:10.2172/230530 fatcat:xtiqd4v3ljdyzhbbhnknqbwbvy