Page:Journal of the Optical Society of America, volume 30, number 12.pdf/34

IV and VI). For dominant wave-length constant, this ratio is the same as the ratio of excitation purities given in Eq. [8], and for minor deviations in dominant wave-length it is closely equivalent.

In Fig. 8 are plotted the "ideal" trichromatic coefficients of the colors, computed from Eqs. [7] and analogous equations derived from Eqs. [8]; data for Munsell values 2/, 4/, 6/, and 8/ are shown. In Fig. 8 are also plotted the 1926 data for the actual samples, these data being indicated by small triangles and circles (as in Fig. 4) The difference between the sample data and the psychophysical data for the same Munsell notation are shown by the dotted lines which connect these respective pairs of points.

Fig. 7. Comparison of the 1919 and 1926 experimental data with values computed from the psychophysical relations. For the five principal colors the relations are as expressed in Eqs. [7] and [8] and as given in the abscissa legend. For the five complementary colors, analogous relations for $x_{V/-C}$, $y_{v/-c}$ and $P_{e(V/-C)}$ were used, based also on $x_{5/5}$, $y_{5/5}$ and $P_{e(5/5)}$; this explains why the dashed curves do not pass through the point, 1, 1 as do the continuous curves. While there is rough agreement between data and curves, large individual deviations may be noted.

It may be seen from Fig. 7 that there is rough agreement between the curves and the plotted points, although the large erratic deviations in some cases make a mental averaging of the data difficult. For certain of the colors it is apparent that the 5/5 sample on which the curves are based is not too well representative of the other colors. It may be seen that there is no certain average difference between the 1919 and 1926 data. Reference to Fig. 8 shows certain trends not apparent from Fig. 7. Figure 8 shows the increasing departures of the experimental data from the psychophysical system as one departs from value 5/, either higher in value through 6/ and 8/, or lower in value through 4/ and 2/; a distinct tendency is shown for the chromas of the lowest Munsell value to be too weak to fit the psychophysical relation, and for the chromas of the highest Munsell value to be too strong to fit this relation.

It may therefore be concluded that the Atlas papers fail to follow the disk-mixture rule resulting in Eq. [11]. The deviations are not merely erratic, as would be expected from the technical difficulties of reproducing the colors by pigments; but also, for both high and low Munsell values, the deviations show consistent tendencies and indicate that selection of these colors was not made solely on the basis of disk mixture.

Tests for Conformity to A
Pyschological System

Most people who have used the Munsell system have taken A. H. Munsell at his word, and have found the system to be a workable approximation of one "built up by equal and decimal steps of sensation." That it could be improved upon is indicated by the fact that the Munsell Research Laboratory was established to develop data upon which such an improvement could be based. Much work was done in the 1920's toward this end (1), with the result that in 1929 the Munsell Book of Color was published (14). Although individual papers of the Book of Color differ somewhat from those of the Atlas, the only important regular change is that the relation, $V^{2}=k(100Y)$, is replaced by a some what less simple relation.