A possible strategy is to include an additional term P in the previous development, requiring that K = K 0 + P K 0 ′ + P 2 K 0 ″ . Solving this differential equation gives the equation of the second-order Murnaghan: P ( V ) = 2 K 0 K 0 ′ [ Γ Γ K 0 ′ ( V 0 V ) Γ Γ + 1 ( V 0 V ) Γ Γ − − 1 − − 1 ] − − 1 where Γ Γ 2 = K 0 ′ 2 − − 2 K 0 K 0 ″ > 0 . Found naturally in the first order equation taking K 0 ″ = 0 . Developments to an order greater than 2 are possible in principle, but at the cost of adding an adjustable parameter for each term.