332 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS chosen on the basis of the spectrophotometric curve. For example, if an attempt were made to match the color shown in Fig. 1 with a powder containing black in place of ultramarine blue, a curve similar to that shown in Fig. 4 would have been obtained. Notice that the flat curve of the black as shown in Fig. 2 produces a flatter curve than does the blue in region 600 to 700 rim. Thus if black rather than blue had been used, only a metameric match to the powder the curve of which is shown in Fig. 1 would have been obtained. It might be a satisfactory match under one light but not under another. On the basis of the spectro- photometric curve, then one should attempt to match the sample with blue rather than black as the dulling component. Although the choice of pigments required to match the color of Fig. 1 is fairly obvious from the curve shapes, the choice is frequently not this apparent and becomes clear only after quantitative calculations have been made. Determination of the amount of pigment required is usually based on the Kubelka-Munk (1) theory. The basic relationship may be expressed in the following equation, where K/S is the ratio of the coefficient of ab- sorption to the coefficient of scatter and R is the reflectance. (1 - R) 2 K/$ - This equation is true for an opaque material at any given wavelength of light. It may be assumed that the value K/S is proportional to the per cent concentration of colored pigment relative to white pigment in the material and that the K/S value in a mixture of pigments is a simple additive function of the K/S values for the individual pigments. These assumptions are described mathematically in equation 2 and are valid except for colors in which the white pigment content is very low. K/&u = C•tK/S• + CBK/Si• + CcK/Sc + K/Sw The values K/SA, KISs and K/So are values for unit concentration of pigments A, B, and C in white and CA, Cs, and Cc are the concentrations of the pigments in the mixture. K/Sw is the value for the white alone K/S• is the value for the mixture. All of the K/S values, of course, are for the same wavelength. By the use of this equation, the K/S value for a specified mixture of pigments can be predicted, providing the K/S values for the individual pigments at unit concentration are known. Equation 1 may then be used to compute the predicted reflectance at the

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