TRISTIMULUS COLOR MEASUREMENTS IN FADING STUDIES 370 •oo GREEN (-'5 D4 ) -- ......... 396 .' CONTROL • 0 // .:•'" •,. ' /I 6 o .'j•- • i/! :.., .. ...r..),r ¾x.. i .."1 C.:-'...:'.... ' "/, •' '•.',, //I V ":.• / ".:x t i "..:x / / '...'.5, ,. i 2O i i i i i I I i I I I I I I I •,80 460 540 620 700 WAVELENGTH (MILLIMICRONS) Figure 9. Reflectance measurements of compacts colored with a combination of water-soluble blue and yellow dyes. The numerals refer to the number of Langley units of direct sunlight exposure for each compact It may be of value to plot the chromaticity coordinates to see if the larger change in color can be accounted for by a shift in the chromaticity or if the main change is a change of lightness of the color. These considerations are of importance in many instances. There are cases in which an on-hue fading can be tolerated within relatively wide limits while an off-hue fading will be a cause for rejection. In other cases the chromaticity limits may be asymmetrical around the object's color. Mackinney and Little (3) point out that butter is a case in which the acceptability limit is unlike that of the perceptibility ellipsoid. Fairly wide variations from yellow to orange will be tolerable, but the slightest shift from yellow to a greenish tinge would be a cause for re- jection. These instances, and there are many of them, tend to compli- cate a rigorous study of colorant fading, but they are of practical impor- tance. It is axiomatic that one tries to use the simplest measurement as long as it correlates with visual observations.

380 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS 'øø f :• 4o 580 gREEN (5D5) --CONTROL 5O ........ I I I I I I I I I I I I I I i I 460 540 620 700 •,¾AVE IE NGTH (MILLIMICRONS) Figure 10. Reflectance measurements of compacts colored with a green aluminum lake. The numerals refer to the number of Langley units of direct sunlight exposure for each compact One way to follow the progress of the color changes is to calculate the "absorbance" value at the point of minimum reflectance. To use the negative log of R to follow the progress of the color change is to assume that R is a linear function of the colorant concentration. This has been shown not to be the case by a number of workers in the fidd of color measurement. The relationship of colorant concentration to reflectance was developed from theoretical and empirical considerations by Kubelka and Munk among others. Reflectance is shown to be related to colorant concentration by the use of their formula: where K is the absorption coefficient and S is the scattering coefficient. A second way of following the color change would be to use the values of the Kubelka-Mur•k equations. This technique assumes, on an