An interrelation among the virial coefficients for temperatures between about 1.0 and 2.7 times the critical temperature is derived from the experimentally observed linearity of the temperature, T, versus the density, p, at constant K = (Z-1)/p, where Z is the compressibility factor. This relates higher virial coefficients at a given T to the temperature dependence of the previous coefficients at that T. The experimental linearity of the constant-K (ISOK) lines is confirmed for nitrogen, from which accurate values of B and C, the second and third virial coefficients, are derived. The new interrelation is then used to find the fourth virial coefficient, D, for nitrogen in this T range (120-340 K). It is also shown that the Lennard-Jones 6,12 intermolecular potential does not obey this interrelation because its ISOK lines are not linear, and therefore it cannot represent the PpT behavior of nitrogen or other common gases. (c) 2005 Elsevier B.V. All rights reserved.