We explore the quasiuniversal behavior of the function Phi(i,j,t) = f(i,j,t)/N(i,j,t) in binary nucleation, where f(i,j,t) and N(i,j,t) are the nonequilibrium and equilibrium cluster concentrations, respectively. The simple, regular patterns that are formed by this function during both the transient period and at steady state suggest that the contour lines of constant Phi form one half of a natural curvilinear coordinate system that underlies the binary nucleation process. In this paper we present the Phi-Line patterns for binary systems that display a wide range of liquid phase nonideality. Quantitative comparisons between analytical expressions for the angle that del Phi makes with the component A axis and for the spacing of the Phi contour lines give good agreement with the values derived from the numerical solution of the binary kinetics equations. The insensitivity of the Phi-line patterns to changes in the gas phase activities of the nucleating species can be better understood by writing the binary kinetics equations with the evaporation rate coefficients as the "difffrsion coefficients." In this form it is easy to see that the equations only depend weakly on the actual gas phase compositions.