Page:Journal of the Optical Society of America, volume 33, number 7.pdf/69

 shapes of these sections appear strange, but those at the lower value levels make some suggestion of the shape of the plane to which Spencer (10) reduced the MacAdam data from the Nutting observations (11). Figure 3 shows five plane vertical sections spaced, roughly, according to the five principal Munsell hues and their complementaries. The dotted lines on the planes in Fig. 2 and Fig. 3 give a good idea of size and shape relative to the solid that can be constructed of available Munsell samples.

Estimates have been made of the total number of perceptibly different colors, that is, the volume of the psychological solid graduated in terms of the differential threshold or of the just noticeable difference. In general, the size of the estimate has increased with the passage of time. Titchener's figure in 1896 was about 33,000 (12) while Boring's in 1939 was 300,000 (13). Since these writers did not distinguish between solids for surface colors and for illuminant colors, their estimates may be taken as maxima. Judd (2) recently estimated that about 10,000,000 surface colors are distinguishable in daylight by a trained observer.

The present model for liminal differences, Fig. 1b, would seem to provide a fair basis for a new estimate. Table 1 shows numbers that total 5836 full chroma steps for 40 hues spaced 2.5 hue steps apart, and nine values spaced one value step apart. Representative difference limen figures for chroma, hue, and value, are 0.2, 0.5, and 0.02 (9), respectively. Since these figures are in terms of the corresponding scale units: 1 chroma step≐5 just perceptible increments, 2.5 hue steps≐5 just perceptible increments, and 1 value step≐50 just perceptible increments. Multiplying the given number of chroma steps by these products, we have: 5836×50×5×5=7,295,000 which does not include the extreme space near 0/ and 10/ value. If this result is increased somewhat to include the extremes, and rounded to 7,500,000, we have an estimate of the number of surface-colors that may be distinguished under the best observational conditions (Fig. 1b). If this number is divided by 4, the result will be 1,875,000, which roughly corresponds to the number expected to be distinguished under the more usual observational conditions of visual color matching work (Fig. la).

(1) L. T. Troland, ''The Principles of Psychophysiology. I. The Problems of Psychology; and Perception'' (Van Nostrand, New York, 1929).

(2) D. B. Judd and K. L. Kelly, “Method of designating colors,” J. Research Nat. Bur. Stand. 23, 355 (1939).

(3) D. B. Judd, “Color systems and their irter-relation,” Illum. Eng. 36, 336 (1941).

(4) S. M. Newhall, “Preliminary report of the O.S.A. subcommittee on the spacing of the Munsell colors,” J. Opt. Soc. Am. 30, 617 (1940).

(5) S. M. Newhall, D. Nickerson, and D. B. Judd,“Final report of the O.S.A. subcommittee on the spacing of the Munsell colors,” J. Opt. Soc. Am. 33, 385 (1943).

(6) E. Q. Adams, “X-Z planes in the 1931 I.C.I. system of colorimetry,” J. Opt. Soc. Am. 32, 168 (1942).

(7) D. L. MacAdam, “Maximum visual efficiency of colored materials,” J. Opt. Soc. Am. 25, 361 (1935).

(8) Dorothy Nickerson, “The specification of color tolerances,” Textile Research 6, 505 (1936).

(9) B. R. Bellamy and S. M. Newhall, “Attributive limens in selected regions of the Munsell color solid,” J. Opt. Soc. Am. 32, 465 (1942).