The linear isotherm regularity (LIR) for dense fluids is used to derive another regularity which is the isotherm [(partial derivative E/partial derivative v)(T)/rho RT]v(2) as a linear function of rho(2), where E is the molar internal energy, (partial derivative E/partial derivative v)(T) is the internal pressure, and rho is the molar density (inverse of the molar volume v). The analytical expressions for the parameters of the latter regularity are obtained in terms of LIR parameters and reported for argon.