A method previously developed to evaluate quantitatively the relationship between intermolecular potential functions and individual macroscopic properties is extended to the simultaneous fit of all possible pair combinations of these properties. As before the relationship between function families available has been clarified. New results from this investigation give important information1on the possible simultaneous fit of a simple function to more than one property. The function families studied were the m-6, Kihara, exp-6 and Morse functions. A reduced temperature range was found over which the simultaneous fit to pairs of properties is insensitive to the potential function. When a transport property is involved, this range is given by 2.0 < T*12-6 < 5.0, while if only equilibrium properties are involved, this range becomes 2.0 < T*12-6 < 10.0. Quantitative limits are given for the experimental error which can be tolerated without masking the sensitivity to the potential function outside these ranges.