Srinivasan's criterion states that, for ill pure fluids, the saturation functions phi(1) = (1 - T(1))P(r) and phi(1)* = (1 - P(r))T(r) (with T(r) = T/T(c) and P(r) = P/P(c), T(c) and P(c) being the temperature and pressure at the critical point) in the vapor-liquid coexistence region present maxima at two different temperatures T(r1) and T(r1)* within a small spread of values: T(r1) approximate to 0.85 to 0.9 and T(r1)* approximate to 0.71 to 0.76. In this paper, we study this criterion for 51 fluids, including quantum fluids ((3)He, (4)He, and H(2)) and normal alkalies C(n)H(2n+2), with n <= 40. We find that T(r1) approximate to 0.77 to 0.93 and T(r1)* approximate to 0.64 to 0.82. Correlations between the values of these maxima. (T(r1), phi(1,max)) and (T(r1)*, phi(1,max)*), are derived depicting their mutual dependence. We also find that the values of the maxima can be accurately predicted in terms of the Pitzer acentric factor omega. These predictions are checked against additional data for 1214 fluids.