phase to coexist with the prevalent gaseous phase. Now, if we had a term to pull the PVT isotherm down in the liquid phase, and a terms to push it back up, a solid phase could be created, as these two terms producing another S-shaped bend between liquid and solid. It was demonstrated that such an S shaped bend could be synthesized using a -function like Lorentzian function over a van der Waals equation of state. Such an equation of state is difficult to manipulate mathematically. In contrast, a virial equation is easier to handle. Argon is used to evaluate realistically this extended virial equation for gas-liquid-solid equilibrium. Data will be analyzed in reduced forms. All PVT variables are scaled by their respective critical values. It is expect from the principle of corresponding states that the results would apply to other well behaved fluids. The relevant data of argon are summarized in the following table: When the variables , , and are replaced by their reduced equivalents, , , and , the virial equation takes the following form: where , , , , and . We will be concerned mostly with condition at the triple point of argon, where and from an earlier study. must be slightly larger than the volume of solid argon, 0.33, and must be between the volumes of liquid and solid argon. Initially, is set to the volume of solid, to produce the last sharply rising edge of the isotherm where solid phase appears at very low volume. The exponential must be then determined so that the valley in the n-2n potential must fit between the volumes of solid (0.33) and liquid (0.378). After the exponential n is determined, the value of can be adjusted to satisfy the Gibbs Rule, which requires that the Gibbs free energy of liquid phase and that of solid phase must be equal under the triple point temperature and pressure. To produce a solid phase in argon, the exponential value n must be very large, larger than 20; otherwise, the PVT isotherm would not bend to an S-shape between liquid and solid. The best estimation is that n = 30, , , and . The isotherm is shown in the right figure, in which three virial terms are plotted separately for clarity: In this figure, represents the sum of the first three virial terms, of the cubic virial equation, and it