In this paper, we derive a new regularity for dense fluids, both compressed liquids and dense supercritical fluids based on the Lennard-Jones (12-6) potential function and using speed of sound results. By considering the internal pressure by modeling the average configurational potential energy, and then taking its derivative with respect to volume, we predict that isotherm [(partial derivative E/partial derivative V)(T)/rho RT]V-2 is a linear function of rho(2), where E is the internal energy, (partial derivative E/partial derivative V)(T) is the internal pressure, and rho = 1/V is the molar density. The regularity is tested with experimental data for ten fluids including Ar, N-2, CO, CO2, CH4, C2H6, C3H8, C4H10, C6H6, and C6H5-CH3. These problems have led us to try to establish a function for the accurate calculation of the internal pressure based on speed of sound theory for different fluids. The results of the fitting show limited success of the pure substances. The linear relationship appears to hold from the lower density limit at the Boyle density and from the triple temperature up to about double the Boyle temperature. The upper density limit appears to be reached at 1.4 times the Boyle density. The results are likely to be useful, although they are limited.