336 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS of predicting a pigment formula to •natch a given color. If one tries to match the color specified in Fig. 1, for example, one can guess at a formula, compute the curve, and compare it with Fig. 1. On the basis of the differences between the predicted and desired curves, one can estimate a new formula and try again. By successive trials, one can eventually arrive at a pigment formula for which the predicted curve would be identical with the desired curve and this formula would then be the predicted formula for matching the sample. The difficulty of course, lies in the amount of time required to make these calculations. It is at this point that computers can solve the problem. PRACTICAL USE OlV THE COLORANT MIXTURE COMPUTER The Davidson and Hemmendinger Colorant Mixture Computer, COMIC, is a high-speed computer designed specifically for solving equa- tions equivalent to equations 2 and 4. The control panel is shown in Fig. 5. Values of K/S for the individual pigments to be used in match- Figure 5. Control panel of the Colorant Mixture Computer ing are adjusted in individual plug-in boxes, five of which can be placed into the computer at one time. These plug-in boxes are labeled "m" in the figure and are often referred to as "primaries." Usually a box is available to represent each of the pigments which might be considered for a match, and these boxes are set up before the computer is used for any matching problems. These K/S values are derived from the spec- trophotometric curves of mixtures of the colored pigment and white similar to those shown in Figs. 2, 3, and 4. Since the computer can

INSTRUMENTATION IN COSMETIC COLOR CONTROL 887 handle the values for 16 wavelengths, the values chosen are usually at 20 nm intervals from 400-700 rim. The standard to be matched is measured at the 16 wavelengths, and the K/S values are set on the dials labeled "f" in Fig. 5. On the oscillo- scope tube "h" 16 dots appear. These dots represent the spectrophoto- metric curve of the standard to be matched. The operator first chooses the pigments he wishes to try and inserts the plug-in boxes representing them. If by adjusting the concentration dials "p" he can bring all of the dots down to the zero line, he has chosen correct pigments for a non- metameric match, and the required amounts will appear on the concen- tration dials. The position of the dots is actually a display of the dif- ference between the solution of 16 equations similar to equation 2 and the K/S values for the standard. When the dots are all on the zero line, the differences between the predicted K/S values and the desired K/S values are zero, indicating that the spectrophotometric curve predicted for the mixture of pigments is the same as that of the standard to be matched. Figure 6 presents an example of use of the computer for matching a color similar to that shown in Fig. 1. The pattern of dots on the oscillo- scope tube are shown for each step in the match. Figure 6a shows the position of the dots representing the spectrophotometric curve of the standard to be matched. Since this is an absorption curve, it is in- verted with respect to the normal spectrophotometric curve shown in Fig. 1. On the basis of this curve the operator decides which pigments to try. He chooses a red oxide, Mapico yellow, and ultramarine blue he plugs the boxes representing these pigments into the computer and adjusts the concentration dials to bring the dots onto the straight line. Several steps in this process are illustrated in Figs. 6b, c, and d. Addi- tion of the blue by means of the appropriate concentration dial adjusts the dots in the long wavelength region of the spectrum addition of the red brings the dots in the middle of the spectrum down to the line and, finally, addition of yellow straightens out the line in the short wavelength region at the left. In this case, the operator chose the proper pigments, and therefore all of the dots can be brought to the zero line. This indicates that a nonmetameric match to the standard may be made with the pigments chosen, and the required amounts of each pigment are shown on the concentration dials. However, if the operator had chosen to dull the color with a black instead of the blue, he would have found it impossible to bring all of the dots down to the zero line. In other words, no values of concentration could have been found which would permit