Page:Journal of the Optical Society of America, volume 30, number 12.pdf/27

 described by Mr. Munsell when he said (9) in 1911, “‘The solid having been built up by equal and decimal steps of sensation ...” or the psychophysical system which he implies in other places. To this end we shall compare the color specifications computed from the 1919 and 1926 measurements both with the psychophysical system and with the psychological system represented by the most adequate data that are available.

Relation between Munsell value and apparent reflectance

The value scale was the first of the three “color dimensions” to be developed by Mr. Munsell; and because he found early in his studies the relation between reflectance and value (8), he developed the Munsell daylight photometer on which value was  thereafter always measured in making up the Munsell Atlas papers. He selected the cat’s-eye form of shutter because it meant that a psychologically photometer scale. The amount of light (the photometric scale) of the Munsell photometer varies in proportion to the square of the diagonal of the diaphragm opening and, since Munsell Atlas papers were all measured on this photometer, it is to be expected that $$V^2$$ will equal point $$Y=1.0$$, $$V^2=100.0$$ is well representative of $$k(100 Y)$$ where $$V$$ is Munsell value, $$Y$$ is the the data as a whole. The fact that this line luminous apparent reflectance relative to MgO (hereafter termed simply the reflectance), and $$k$$ is a constant close to unity. This was demonstrated in the 1919 report (2) and is also pointed out by Tyler and Hardy (11).

To test this relation further we have plotted in : A straight line with value of $$k=1$$; the straight line given in Bureau of Standards Technologic Paper No. 167 as representative of the relation derived from the nine neutral samples therein described; the average values of $$Y$$ for Munsell values 3/, 5/, and 7/, as derived from Bureau of Standards Technologic Paper No. 167 in accordance with  of the present paper (1919 data); the average values of $$Y $$ for the respective Munsell values from 2/ to 8/, for both diffuse-normal and 45°-normal conditions, 10 values of Y entering into each of the average values of Y for each of the two illuminating-viewing conditions, these data taken from Tables  and  (1926 data); and the extreme individual values of Y for the respective Munsell values, taken from Tables,  or.

From we may draw several conclusions: The relation $$V^2=k(100 Y)$$ is followed approximately by both the 1919 and 1926 data, although particular samples show large deviations. Both the 1919 and 1926 data indicate that $$Y$$ has a small positive value (0.005 to 0.01) when the Munsell value is zero; black, in the Munsell Atlas, therefore corresponds to a luminous apparent reflectance of 0.5 to 1.0 percent. While the straight line representing the neutral samples of the 1919 data falls under the line $$k=1$$, a majority of the points representing the chromatic samples of the 1926 data fall above this line, satisfactory scale could be read directly on the and it is obvious that a straight line passing through the point $$Y=0.007$$, $$V^2=0.0$$ and the $$V^2=100$$ passes through the point $$Y=1.0$$, $$V^2=100$$ indicates that white, in the Munsell Atlas, is represented by fresh magnesium oxide. There are slight indications that individual values of $$Y$$ for any given Munsell value may be high or low as a group. The data for $$V=6$$ are the most definite in this respect. The data also show that the colors of certain hues are uniformly different from others in Munsell value.

Relation between Munsell hue and dominant wave-length

If the samples representing the Munsell color system conform to the simple psychophysical definition of hue by disk mixture, the points representing all samples of the same Munsell hue designation and its complementary will plot on the Maxwell triangle along a straight line passing through the neutral point (11). To test