Page:Journal of the Optical Society of America, volume 30, number 12.pdf/33

their 5/5 complementaries computed by Eqs. [5] when the tristimulus specifications of the illuminant are used for $X_{5/0}$, $Y_{5/0}$, and $Z_{5/0}$. It is concluded that the irregularity of the 5/5 locus computed about the illuminant point cannot be ascribed to a disparity between the illuminant used in the computations and that used in the selection of the colors of the Munsell Atlas.

Second, perhaps the Munsell gray samples are sufficiently nonselective in the yellowish sense to account for the difference. Some of those illustrated in Bureau of Standards Technologic Paper No. 167 (2) are slightly yellowish, but only N 7/, N 8/, and N 9/ show any important selectivity. Even the yellowest of these, N 9/ (x=0.3167, and y=0.3256 for I.C.I. Illuminant C), is not sufficiently selective to bridge the gap between the color of the illuminant and that of equal-area disk mixture of the five principal colors. Hence the average color of the Munsell neutral samples, at least in 1919, is not sufficiently different from that of the illuminant to account for the difference.^[1]

Third, it is possible that one or more of the five principal colors, by the time they were measured in 1919, may have changed sufficiently to shift the mixture point from the illuminant point to the DM point. If the five colors of the original system did spin to match a nonselective neutral at the time of their selection, then a regular system, of the sort represented here, would have resulted. The DM point would at that time have been identical with the illuminant point. There seems to be no way to test this possibility, but it is pointed out elsewhere that no certain changes in the samples have occurred between 1919 and 1926.

TABLE VI. Specifications of the five principal Munsell colors, for the Munsell N 5/ given by equal-area disk mixture of these five colors, and for the complements of these five colors at 5/5. The tristimulus specifications of each color have been multiplied by a factor to make Y=0.2500.

Munsell Not- ation	Trisimulus Specifications			Trichromatic Coefficients		Dominant Wave Length and Purities (Reference Point: z=0.3234, y=0.3255)
	X	Y	Z	x	y	A†	Pe‡	Pe§
R 5/5	0.31298	0.2500	0.20018	.0.41011	0.32759	610.6	25.7	25.3
Y 5/5	.24459	.25000	.09613	.41405	.42321	576.8	64.2	53.4
G 5/5	.18454	.25000	.20198	.28992	.39276	510.5	28.1	13.3
B 5/5	.21634	.25000	.42235	.24344	.28131	484.0	20.7	31.5
P 5/5	.28326	.25000	.42761	.29480	.26018	568.c	0.8	19.4
NDM 5/	.24834	.25000	.26965	.32336	.32553	—	0.0	0.0
BG 5/5	.18370	.25000	.33912	.23770	.32349	491.0	0.0	0.0
PB 5/5	.25208	.25000	.44318	.26668	.26448	476	9.1	25.4
RP 5/5	.31214	.25000	.33732	.34703	.27794	519 c	10.2	23.3
YR 5/5	.28034	.25000	.11694	.43311	.38623	585.8	56.9	48.9
GY 5/5	.21342	.25000	.11170	.37109	.43469	568	58.6	44.8

*r4 The reference point for this system is the neutral point N 5/ resulting from equal-area disk mixture of the five principal 5/5 samples; it differs slightly from the point representing I.C.I. Illuminant C.

†r5 Dominant wave-lengths were read from a large-scale (x,y)-plot of the spectrum locus by extending straight lines from the point representing the Nm mixture through the point representing the 5/5 sample in question to the spectrum locus.

†r6 Values of $P_{e}$ were calculated from the Judd (18) formula, except that for nonspectral colors the line connecting the extremes of the spectrum was taken to represent unit purity. With these values of Pc(5/5), Pe for all other samples in this psychophysical system can be calculated from Eq. [10].

§ Values of $P_{c}$. were calculated from a variation of the Hardy formula (7, p. 59) which results in: $P_{e}=Pc_{(y/y\lambda ,)}$. $P_{e}$ for all other samples in this psychophysical system can be calculated from Eq. [8].

We may now proceed by Eqs. [8] with a test of the psychophysical nature of the Munsell system exemplified by the papers measured in 1919 and 1926. The curves in Fig. 7 show C/V plotted against the ratio of excitation purities given by Eqs. [8] for the five principal Munsell hues and their complements.^[2] If the measurements of the papers had resulted in dominant wave-length constant for each hue, the desired comparison would be given by plotting, on the same graphs, $C/V$ for each color also against the ratio of excitation purities. Since, as shown in Fig. 5, considerable departure from dominant-wave-length constancy has been found, $C/V$ for each color is plotted instead against the ratio of distances from the neutral (DM) point on the (x, y)-diagram. This distance ratio is given by the expression:

$\left[{\frac {\left(x_{5/5}-x_{5/0}\right)^{2}+\left(x_{5/5}-x_{5/0}\right)^{2}}{\left(x_{V/C}-x_{5/0}\right)^{2}+\left(x_{V/C}-x_{5/0}\right)^{2}}}\right]^{\frac {1}{2}}$

all of whose terms are known (Tables II, III,

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1. It may be noted that equal-area disk mixture of the five principal colors without adjustment to Y=0.2500 yields $x{5/0}$=0.3213 and $y_{5/0}$=0.3262, not importantly different from the trichromatic coefficients obtained with this adjustment. It is curious, however, that the neutral point obtained by disk mixture of the five principal colors without adjustment, and the neutral point given by N 9/, both give better representative reference points for the dominant wave-length lines than do either I. C. I. Illuminant C or the disk-mixture (DM) point with the adjustment. The most symmetrical shape for the area defined by the five principal colors and their complementaries is, however, given by the DM point.
2. In preparing Fig. 7 the data and curves for the complements were based on equations analogous to Eqs. [7] and [8] (derived from Eqs. [5]) which express $(xv/-c)$, $y/-C$ and $P_{e(v/-c)}$ in terms of $x_{(5/5)}$, $y_{(5/5)}$ and $P_{e(5/5)}$. This explains why the dashed curves of Fig. 7 do not pass through the 1,1 point, and further illustrates that the whole psychophysical system can be expressed in terms of the five principal colors.