Page:Journal of the Optical Society of America, volume 30, number 12.pdf/51

supraliminal sense magnitudes or intervals (17, 19, 21, 47, 57, 72-78).^[1] The one magnitude or interval is taken as standard and the ratio of the other to it is then estimated directly.

Fig. 2. Recording of estimates made by the simple ratio method

The two forms of this method are applicable to color problems and both were applied in the present review. The first form may be referred to as the simple ratio or $R$ form and represented by the simple operational equation

${(C_{2}/C_{1})}_{A}=R_{a}$

in which $C_{1}$, represents the color perceived as belonging to the chosen standard; $C_{2}$, the color to be evaluated; $R$, the estimate of the ratio; and the subscript $_{A}$, the attribute with respect to which the estimate is made. Thus, the given color $C_{2}$, is judged equal to $RC_{1}$, with respect to $_{A}$. Suppose that $C_{1}$ and $C_{2}$, represent two surface-color perceptions and the observer’s task were to estimate relative lightness. He would compare the two colors directly with each other and report a quantitative judgment concerning the fraction or multiple which the lightness of $C_{2}$ is of $C_{1}$;. In case of surface-color perception, as when one views the Munsell samples, $_{A}$ may become either $_{H}$, $_{S}$ or $_{L}$, according to whether hue, saturation, or lightness is the attribute being estimated. According to the existing O.S.A. definitions (31, p. 213) hue, saturation, and lightness correspond closely to Munsell hue, chroma, and value.

Fig. 3. Recording of estimates made by the difference ratio method.

The second, or difference ratio, method is designated by R’ and represented by the analogous equation

$(|{C_{4}-C_{3}}|/|{C_{2}-C_{1}}|)=R'_{A}$

in which $|C_{2}-C_{1}|$ is the perceived standard difference or interval, $|C_{4}-C_{3}|$ is the difference to be evaluated, and R’ is the estimate of the ratio of intervals with respect to 4, the particular aspect under estimate.

The observer records his estimate either by numbers or by linear extents which seem to him to be in the ratio of the sense magnitudes in question. Perhaps the easiest method is to adjust the relative positions of the samples themselves until the space ratio represents the sense ratio. A more generally practicable recording method, however, is graphically to indicate rather than actually to make, the representative space adjustment. Figure 2 suggests the application of graphic recording to the $R$ form. The observer represents the attributive magnitude of $C$; by a line of convenient length. He then draws a second line, representing $C_{2}$, of such length relative to the first line that the ratio formed by the two lines is the same as the estimated ratio. Figure 3 shows the same kind of recording in case of the $R'$ form of the ratio method. Here the one line is drawn to represent the sense difference or sense distance between $C_{2}$; and $C_{1}$, while the other line is so drawn that its length relative to the first will be the same as $C_{3}-C_{4}$; relative to $C_{2}-C_{1}$.

The difference-form ($R'$) of estimate is more reliable because the perceptual unit is defined by its beginning point ($C_{1}$) and its end point ($C_{2}$), both presented to the observer during the estimate. The analytically simpler form ($R$) implies a beginning point corresponding to zero (zero lightness, or zero saturation), but no sample exemplifying this beginning point is present. Therefore greatest reliance was placed on estimates by the difference-form ($R'$).

The use of the ratio method seems peculiarly

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1. Reference 57 contains a detailed discussion of the ratio method and its application to the spacing problem; and much of that material has been adapted and included in the present report. Figs. 2 and 3 of the earlier paper have been reproduced as Figs. 2 and 3 herein.