338 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS (i d • Figure 6. Appearance of the COMIC oscilloscope tube during various stages of solving a matching problem a solution of 16 equations of the form of equation 2 so that all 16 pre- dicted K/S•u values were equal to the K/S values of the standard to be matched. The appearance of the line of dots would have been similar to that shown in Fig. 6e. If this situation arose, the operator would select a different set of pigments and repeat the operation until an appropriate combination had been selected. The first trial formula will not, of course, produce a perfect match to the standard. The size of the color difference will depend upon many factors, including the accuracy of the calibration of the primaries, the degree of control over the dispersion of the pigments, and the degree to which the equation truly represents the process. Color differences of from three to eight MacAdam (2, 3) units can be expected on the first trial. Although in most cases a mismatch of this magnitude would be larger than could be tolerated, it is sufficiently small so that computed adjustments will produce an acceptable match after one or two cor- rections. Adjustments to the first trial may be made either spectrophotometri- cally or colorimetrically. If a spectrophotometric correction is to be

INSTRUMENTATION IN COSMETIC COLOR CONTROL 339 made, the reflectance values of the trial sample are converted to values and placed on the dials labeled "g" in l½ig. 5. The values for the standard are, as before, placed on the dials labded "f." The dots on the cathode ray tube take up positions representing the differences in K/S values between the standard and the trial. Appropriate pigments are then added to, or subtracted from, the formula by means of the concentration dials and polarity switches, labeled 'j" in l½ig. 5, until the dots are all on the zero line. The formula adjustments are then read from the concentration dials, and the signs of the adjustments are given by the polarity switch positions. Color adjustments may be made more rapidly and in most cases more accuratdy on the basis of tristimulus values if the color adjustment is small. The differences in tristimulus values (g.X, g. Y, and ZXZ) between the standard and sample are obtained from a colorimeter or by computa- tion from the spectrophotometric curves using equations 3 or 4. These values are placed on the computer dials labeled "c" in Fig. 5. Sixteen values for the standard are then placed on the dials labeled "b." These are known as dR/d(K/S) values (4) and are used to convert the voltage differences in the computer which represent K/S differences into reflec- tance differences, g.R, for use in equation 4 with which the predicted values of ZXX, zXY, and •Z are computed for any pigment alteration. Three meters, labeled "a," are then hulled by means of the concentration dials and switches to obtain the formula correction. If more than three colored pigments are used, the formula is not unique that is, many dif- ferent combinations of pigment ratios will produce a colorimetric match. 0nly one of these combinations will produce a nonmetameric (or spec4 trophotomeric) match. In this case, the colorist must reduce the prob- lem to control of three pigments, either by using only three pigments to make his adjustment or by specifying one or more of the pigment ratios. So far it has been assumed that the operator could find a combination of pigments which would produce a nonmetameric match to the stand- ard. This is not always possible. Perhaps the pigments which will produce a nonmetameric match are not certified or are too expensive. Some other combination must be used, and a metameric match may be required. In this case, the operator will be unable to bring all of the dots down to the zero line. In order to determine the correct formula, he must now place the dR/d(K/S) values for the standard on the dials labeled "b" and must set the zXX, ZXY, ZXZ dials, labeled "c," at zero. The K/S values for the standard are as before placed on the dials la- beled "f." Now the operator lines up the dots on the zero line as nearly