In previous papers a correlate for lightness (L) was found in terms of CIE-tristimulus values for colors of approximately constant luminous reflectance (Y). L could be expressed by a second degree equation with X, Y, Z as variables. In the present study about 100 samples were selected to cover the gamut of existing surface colors. The lightness-equivalent neutrals were estimated by three observers for these colors under the same conditions as described in a previous paper. The original type of equation could not be used to fit the observational data because of the large differences in luminous reflectance among the samples. However, the L/Y ratios could be expressed by a second degree equation with chromaticity coordinates x, y as variables. This type of equation appears to be valid for all reflecting surface colors.
C. L. SANDERS and G. WYSZECKI, "L/Y Ratios in Terms of CIE-Chromaticity Coordinates," J. Opt. Soc. Am. 48, 389-391 (1958)