On the assumption of a color space of constant negative curvature, von Schelling has given simple formulas for the color metric coefficients. An attempt has been made to fit such formulas to newly available color-discrimination data for 12 normal observers. A least-squares analysis indicates that Y should be replaced with the quantity, Y′ = Y-0.085X+0.011Z, in the special role assigned to luminance by von Schelling. Corresponding to this change, coordinates x’=X/(X+ Y’+Z), y’= Y’/(X+ Y’+Z) yield the simplest formulas for the coefficients of the expression for color difference: ΔS=(g11Δx’2+2g12Δx’Δy’+g22Δ′2+g33 Δy2/y2)½. Least-squares fitting of the experimental data to von Schelling’s formulas yielded: g11=g33/(10x’2-6.886x’+2.083+2.5y’-16.66x’y’+19.6y’2). g12=g11(0.3443-x’)/y’. g22=g11[0.09+(0.3443-x’)2]/y’2. These formulas are the best approximations obtainable on the assumption of a color space of constant negative or zero curvature. However, they give such poor approximations to the experimental data that it is concluded that the assumption of a color space inherently more complicated than a space of constant curvature would be required to fit the data to a closeness commensurate with the experimental reproducibility.
D. L. MACADAM, "Analytical Approximations for Color Metric Coefficients," J. Opt. Soc. Am. 47, 268-274 (1957)