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  1. The relation between value and brilliance is given in the first paper of this series, note 1. See Munsell, Sloan and Godlove, J. Opt. Soc. Am. 23, 394 (1933).
  2. L. T. Troland et al., Report of the Colorimetry Committee of the Opt. Soc. of Am., 1920–21; J. Opt. Soc. Am. and R. S. I. 6, 539 (with footnote) (1922).
  3. Cobb, 1913 to 1916. See reference 20 of the first paper.
  4. See Kohlrausch; Tagessehen, Dämmersehen, Adaptation, I. Allgemeines über Umstimmung und "Farbenkonstanz der Sehdinge," in Handb. d. normalen u. pathologischen Physiol. 12, 2nd half, Receptionsorgane, II, p. 1502; Berlin (1931).
  5. Delboeuf, Bull. de l'Acad. royale de Belgique 34, 250, 261 (1872).
  6. See the discussion of these laws in the historical section of the first paper of this series (reference 1) and references 12 to 18 of that paper.
  7. Adams and Cobb, J. Exper. Psychol. 5, 39–45 (1922)
  8. In Cobb's observations the stimuli were presented in random order, as is customary in the "method of right and wrong cases." The ordinary method of calculation employed in this method could not be used because (1) the stimuli were changed during the course of the work, and (2) the number of experiments with each stimulus was not sufficient. The method of computing the J. N. D. was based on the table of Fechner, in turn founded on the Gauss law of error, and consisted in "finding the point on the stimulus scale such that the sums of the wrong judgments on either side are equal." Certain approximations were made, but the computation was intended to be such that the probability of seeing the difference "correctly" at the threshold was 0.50, and the threshold was taken as the point where the sums for the cases of appearance of greater brightness on the left half of the field were equal to the corresponding cases for the right half plus cases of appearance of equality (the equal-stimulus cases being actually only 4 percent of the total). The method used, Cobb says "is based on the same assumptions as the classical method of constant stimuli." The J. N. D. obtained by the method described would of course be smaller than that obtained by the method of the present investigation; and it is seen that this is actually the case by comparing the results.
  9. The data by the second method throw less light on this question, since the value scale determined by it was made to agree with the J. N. D. scale at values 2.12 and 9.55.
  10. The more accurate but more tedious least squares determination of the constants was not thought worth while in view of the limitation of the value of such formulae in expressing the experimental data for all backgrounds, and because of the desire to fit the equations to the experimental data exactly at value 5, since here the Cobb data agreed very well with the Munsell J. N. D. data (and better with the Munsell value-step data). The Adams and Cobb equation in its unmodified form could not be fit at two points—the fit at value 10 was not made-since it contains only one arbitrary constant, the other being the reflectance of the background.
  11. See notes 5, 6, and 22 of the first paper of this series.

Troland, L. T.

L. T. Troland et al., Report of the Colorimetry Committee of the Opt. Soc. of Am., 1920–21; J. Opt. Soc. Am. and R. S. I. 6, 539 (with footnote) (1922).

Other

The relation between value and brilliance is given in the first paper of this series, note 1. See Munsell, Sloan and Godlove, J. Opt. Soc. Am. 23, 394 (1933).

L. T. Troland et al., Report of the Colorimetry Committee of the Opt. Soc. of Am., 1920–21; J. Opt. Soc. Am. and R. S. I. 6, 539 (with footnote) (1922).

Cobb, 1913 to 1916. See reference 20 of the first paper.

See Kohlrausch; Tagessehen, Dämmersehen, Adaptation, I. Allgemeines über Umstimmung und "Farbenkonstanz der Sehdinge," in Handb. d. normalen u. pathologischen Physiol. 12, 2nd half, Receptionsorgane, II, p. 1502; Berlin (1931).

Delboeuf, Bull. de l'Acad. royale de Belgique 34, 250, 261 (1872).

See the discussion of these laws in the historical section of the first paper of this series (reference 1) and references 12 to 18 of that paper.

Adams and Cobb, J. Exper. Psychol. 5, 39–45 (1922)

In Cobb's observations the stimuli were presented in random order, as is customary in the "method of right and wrong cases." The ordinary method of calculation employed in this method could not be used because (1) the stimuli were changed during the course of the work, and (2) the number of experiments with each stimulus was not sufficient. The method of computing the J. N. D. was based on the table of Fechner, in turn founded on the Gauss law of error, and consisted in "finding the point on the stimulus scale such that the sums of the wrong judgments on either side are equal." Certain approximations were made, but the computation was intended to be such that the probability of seeing the difference "correctly" at the threshold was 0.50, and the threshold was taken as the point where the sums for the cases of appearance of greater brightness on the left half of the field were equal to the corresponding cases for the right half plus cases of appearance of equality (the equal-stimulus cases being actually only 4 percent of the total). The method used, Cobb says "is based on the same assumptions as the classical method of constant stimuli." The J. N. D. obtained by the method described would of course be smaller than that obtained by the method of the present investigation; and it is seen that this is actually the case by comparing the results.

The data by the second method throw less light on this question, since the value scale determined by it was made to agree with the J. N. D. scale at values 2.12 and 9.55.

The more accurate but more tedious least squares determination of the constants was not thought worth while in view of the limitation of the value of such formulae in expressing the experimental data for all backgrounds, and because of the desire to fit the equations to the experimental data exactly at value 5, since here the Cobb data agreed very well with the Munsell J. N. D. data (and better with the Munsell value-step data). The Adams and Cobb equation in its unmodified form could not be fit at two points—the fit at value 10 was not made-since it contains only one arbitrary constant, the other being the reflectance of the background.

See notes 5, 6, and 22 of the first paper of this series.

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