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  1. The relation between Value and Brilliance is as follows: “Brilliance is that attribute of any color in respect of which it may be classed as equivalent to some member of a series of grays ranging between black and white.” (Report of the Committee on Colorimetry of the Optical Society of America, J. O. S. A. and R. S. I.6, 534 (1922).) Value bears a relation to the color attribute brilliance similar to that which the Fahrenheit and Centigrade scales, as measured with the various (gas, mercury, etc.) types of thermometers, bear to temperature. Value is the practical approach to brilliance afforded by reflection standards, the special case of brilliance so represented having the important difference of corresponding to a constant level of adaptation of the eye. More precisely, value is the brilliance of the colors of a series of standards, varying in reflectance from zero to unity, in such a way that all visual intervals are uniform when viewed on a middle gray background by a light-adapted eye. The standard Munsell value unit is defined as one-tenth the difference in value between a surface of 0 percent reflectance and one of 100 percent reflectance when both are viewed on a background whose reflectance is about 18 percent and illuminated by 22.8 f.c. of daylight (5200°K).
  2. A. E. O. Munsell and et al., Munsell Book of Color, on p. 46, Baltimore, 1929.
  3. F. G. Cooper, Munsell Manual of Color, on p. 33, Baltimore, 1929.
  4. A. H. Munsell, Atlas of the Munsell Color System, Boston, 1915.
  5. The Ostwald scale is of the logarithmic type corresponding to the Weber-Fechner law, considered below; the “Atlas” value scale of A. H. Munsell is of the exponential type presaged by the work of Plateau and others (see below). A third type of law, that of Adams and Cobb considered below, has not been applied to practical value scales.
  6. P. Bouguer, Traité d’optique sur la gradation de la lumiere, p. 51, Paris, (Lacaille)1760. He used the following method. He set up a post between two candles and a white cardboard so that each candle cast a shadow on the latter. Shadow 1 was illuminated by candle 2, and shadow 2 by only candle 1, whereas the remaining area was illuminated by both candles. He varied the distances of the candles until one of the shadows disappeared. This occurred when the relative distances of the two candles was about 8.16 to 1, or such that the intensities of illuminations (as given by the “inverse square law”) was about 1 to 66.67 (or 1.5 to 100). That is, the ratio of the brightness of the screen to that of the remaining shadow was 1.015.
  7. J. H. Lambert, Photometria, Augustae Videlic, 1760. C. A. Steinheil, Elemente der Helligkeitsmessungen am Sternhimmel; Abhandl. k. bayr. Akad. Wissensch., Math.-Phys. Cl. 2, 1 (1837). Arago, Oeuvres completes, Paris, X; 1858. G. T. Fechner, Über ein wichtiges psychophysisches Grundgesetz u. d. Beziehung z. Schatzung d. Sterngrossen, Abhandl. k. sachs. ges. Wissensch., Math.-phys. Kl. 4, 455 (1859). G. T. Fechner, Elemente der Psychophysik, Leipzig; 1860. The last-named obtained the Fechner fraction 0.010.
  8. M. A. Masson, Études de photometrie electrique; Ann. chim. et phys. [3] 14, 129 (1845). E. Kraepelin, Zur Frage der Gültigkeit des Weberschen Gesetzes bei Lichtempfindungen; Phil. Stud. 2, 306–26 (1885). E. Kraepelin, Nachtrag zu der Arbeit u. d. Gültigkeit des Weberschen Gesetzes bei Lichtempfindungen; Phil. Stud. 2, 651–57 (1885). Masson introduced the method of using a series of white disks each with a small black sector. When the disk was rotated a faint gray ring was seen on the white background. The size of the black sector giving a just perceptible gray ring furnished a determination of the Fechner fraction. Later experimenters modified this technique in various ways, in part for the purpose of eliminating certain contrast effects which might modify the results.
  9. A. W. Volkmann, Physiol. Untersuchungen im Gebiete d. Optik 1, 56 (1863). H. Helmholtz, Handb. d. physiologischen Optik, Hamburg and Leipzig, 1886.
  10. H. Aubert, Physiologie der Netzhaut; pp. 52–82 (1865).
  11. J. Plateau, Über die Messung physischer Empfindungen u. d. Gesetz welches die Starke d. erregenden Ursache verknupft, Pogg. Ann. 150, 465–76 (1873).
  12. By way of comparison with the Plateau law, it can be shown that the Weber-Fechner law results from assuming that observers pick a mid-gray in such a way that it gives equal differences (rather than equal ratios) of sensations when compared with black and white; i.e., so that V2−Vm=Vm−V1. Delboeuf, Bull. de l’Acad. royale de Belgique 34, 250, 261 (1872), pointed out that according to the Weber-Fechner law, a small positive value of R corresponds to a negative value of V, and zero value of R to an infinitely negative value of V, which is an absurdity. Further, his results were not entirely independent of the illumination, as required by the Weber-Fechner law.
  13. A. Lehman, Über die Anwendung der Methode der mittleren Abstufung auf den lichtsinn; Wundt’s Phil. Stud. 3, 497–533 (1886). H. Neiglick, Zur Psychophysik des Lichtsinns; Wundt’s Phil. Stud. 4, 28–111 (1888).
  14. P. Breton, Comptes Rendus 105, 426–29 (1887).
  15. J. Merkel, Die Abhangigkeit zwischen Reiz und Empfindund, Wundt’s Phil. Stud. 4, 541 (1888); Wundt’s Phil. Stud. 5, 499 (1889); Wundt’s Phil. Stud. 10, 239 (1894).
  16. Ebbinghaus; Grundzuge der Psychologie, I, 497, Leipzig, 1902. W. Ament, Über das Verhaltnis der ebenmerklichen zu den ubernmerklichen Unterschieden bei Licht- und Schallintensitaten; Wundt’s Phil Stud. 16, 135–96 (1900).
  17. J. Fröbes, Ein Beitrag über die sogenannten Vergleichungen ubermerklicher Empfindungsunterschiede; Zeits. f. Psychologie 36, 304–80 (1904). A. Stefanini, Sulla legge di oscillazione dei diapsson e sulla misura dell’ intensita del suono; Atti della R. Acad. Lucchese 25, 305–400 (1889).
  18. A. König and E. Brodhun, Experimentelle Untersuchungen über die Psychophtysiche Fundamentalform in Bezug auf den Gesichtssinn; Gesammelte Abhandl. z. Physiologischen Optik, p. 135–39. J. Blanchard, The Brightness Sensibility of the Retina, Phys. Rev. 11, 81–99 (1918); obtained results agreeing in general with König and Brodhun’s (and Aubert’s).
    [CrossRef]
  19. P. W. Cobb and L. R. Geissler, The Effect on Foveal Vision of Bright Surroundings, I; Psychol. Rev. 20, 525–47 (1913). P. W. Cobb, The Effect on Foveal Vision of Bright Surroundings, II; Psychol. Rev. 21, 23–32 (1914). P. W. Cobb, The Effect on Foveal Vision of Bright Surroundings, III; J. Exper. Psychol. 1, 419–25 (1916); IV, J. Exper. Psychol. 1, 540–66 (1916).
    [CrossRef]
  20. E. Q. Adams and P. W. Cobb, The Effect on Foveal Vision of Light (and Dark) Surroundings, V; J. Exper. Psychol. 5, 39–45 (1922).
    [CrossRef]
  21. This photometer operated on the “cat’s-eye” principle, that is, the area of the variable aperture through which a reflecting standard was illuminated with decreasing intensity until the sample was matched (or the movement of the brightness indicator) was proportional to the square of the diagonal of the (square) aperture. Equal areas of aperture or equal movements of the indicator corresponded approximately to equal sensation (rather than equal reflection) differences. This relation corresponded further to the simple rule: The percentage reflectance of any one of the ten steps of value in the Munsell “Atlas Value Scale” is obtained by multiplying this value by itself. For example, value 7 gives 7×7 or 49 percent. This earlier Munsell value scale was carefully examined by the U. S. Bureau of Standards, with the results reported by Priest, Gibson and McNicholas (Bur. Stand. Tech. Pap. No. 167, p. 27; 1920) as follows:Value level1/2/3/4/5/6/7/8/9/Value×value149162536496481%B. S. findings249162334466072%Considering the drawbacks of the photometer resulting from its portable construction, the results are very satisfactory.
  22. I. G. Priest, The Spectral Distribution of Energy Required to Evoke the Gray Sensation, ; 1921. In the quotation, the word in brackets has been inserted by the authors.
  23. C. W. Keuffel, A Direct Reading Spectrophotometer, J. Opt. Soc. Am. 11, 407 (1925); see the figure on p. 406.
    [CrossRef]
  24. The strengths of the correcting spheres or cylinders worn by four of the five observers were equal to or less than one diopter. The glasses worn by C. E. B. were O. D. −2.5 sph., −3 cyl. axis 165, O. S. −4.25 sph., −2 cyl. axis 10.

1925 (1)

C. W. Keuffel, A Direct Reading Spectrophotometer, J. Opt. Soc. Am. 11, 407 (1925); see the figure on p. 406.
[CrossRef]

1922 (1)

E. Q. Adams and P. W. Cobb, The Effect on Foveal Vision of Light (and Dark) Surroundings, V; J. Exper. Psychol. 5, 39–45 (1922).
[CrossRef]

1913 (1)

P. W. Cobb and L. R. Geissler, The Effect on Foveal Vision of Bright Surroundings, I; Psychol. Rev. 20, 525–47 (1913). P. W. Cobb, The Effect on Foveal Vision of Bright Surroundings, II; Psychol. Rev. 21, 23–32 (1914). P. W. Cobb, The Effect on Foveal Vision of Bright Surroundings, III; J. Exper. Psychol. 1, 419–25 (1916); IV, J. Exper. Psychol. 1, 540–66 (1916).
[CrossRef]

1904 (1)

J. Fröbes, Ein Beitrag über die sogenannten Vergleichungen ubermerklicher Empfindungsunterschiede; Zeits. f. Psychologie 36, 304–80 (1904). A. Stefanini, Sulla legge di oscillazione dei diapsson e sulla misura dell’ intensita del suono; Atti della R. Acad. Lucchese 25, 305–400 (1889).

1888 (1)

J. Merkel, Die Abhangigkeit zwischen Reiz und Empfindund, Wundt’s Phil. Stud. 4, 541 (1888); Wundt’s Phil. Stud. 5, 499 (1889); Wundt’s Phil. Stud. 10, 239 (1894).

1887 (1)

P. Breton, Comptes Rendus 105, 426–29 (1887).

1886 (1)

A. Lehman, Über die Anwendung der Methode der mittleren Abstufung auf den lichtsinn; Wundt’s Phil. Stud. 3, 497–533 (1886). H. Neiglick, Zur Psychophysik des Lichtsinns; Wundt’s Phil. Stud. 4, 28–111 (1888).

1873 (1)

J. Plateau, Über die Messung physischer Empfindungen u. d. Gesetz welches die Starke d. erregenden Ursache verknupft, Pogg. Ann. 150, 465–76 (1873).

1872 (1)

By way of comparison with the Plateau law, it can be shown that the Weber-Fechner law results from assuming that observers pick a mid-gray in such a way that it gives equal differences (rather than equal ratios) of sensations when compared with black and white; i.e., so that V2−Vm=Vm−V1. Delboeuf, Bull. de l’Acad. royale de Belgique 34, 250, 261 (1872), pointed out that according to the Weber-Fechner law, a small positive value of R corresponds to a negative value of V, and zero value of R to an infinitely negative value of V, which is an absurdity. Further, his results were not entirely independent of the illumination, as required by the Weber-Fechner law.

1865 (1)

H. Aubert, Physiologie der Netzhaut; pp. 52–82 (1865).

1863 (1)

A. W. Volkmann, Physiol. Untersuchungen im Gebiete d. Optik 1, 56 (1863). H. Helmholtz, Handb. d. physiologischen Optik, Hamburg and Leipzig, 1886.

1845 (1)

M. A. Masson, Études de photometrie electrique; Ann. chim. et phys. [3] 14, 129 (1845). E. Kraepelin, Zur Frage der Gültigkeit des Weberschen Gesetzes bei Lichtempfindungen; Phil. Stud. 2, 306–26 (1885). E. Kraepelin, Nachtrag zu der Arbeit u. d. Gültigkeit des Weberschen Gesetzes bei Lichtempfindungen; Phil. Stud. 2, 651–57 (1885). Masson introduced the method of using a series of white disks each with a small black sector. When the disk was rotated a faint gray ring was seen on the white background. The size of the black sector giving a just perceptible gray ring furnished a determination of the Fechner fraction. Later experimenters modified this technique in various ways, in part for the purpose of eliminating certain contrast effects which might modify the results.

1760 (1)

J. H. Lambert, Photometria, Augustae Videlic, 1760. C. A. Steinheil, Elemente der Helligkeitsmessungen am Sternhimmel; Abhandl. k. bayr. Akad. Wissensch., Math.-Phys. Cl. 2, 1 (1837). Arago, Oeuvres completes, Paris, X; 1858. G. T. Fechner, Über ein wichtiges psychophysisches Grundgesetz u. d. Beziehung z. Schatzung d. Sterngrossen, Abhandl. k. sachs. ges. Wissensch., Math.-phys. Kl. 4, 455 (1859). G. T. Fechner, Elemente der Psychophysik, Leipzig; 1860. The last-named obtained the Fechner fraction 0.010.

Adams, E. Q.

E. Q. Adams and P. W. Cobb, The Effect on Foveal Vision of Light (and Dark) Surroundings, V; J. Exper. Psychol. 5, 39–45 (1922).
[CrossRef]

Aubert, H.

H. Aubert, Physiologie der Netzhaut; pp. 52–82 (1865).

Bouguer, P.

P. Bouguer, Traité d’optique sur la gradation de la lumiere, p. 51, Paris, (Lacaille)1760. He used the following method. He set up a post between two candles and a white cardboard so that each candle cast a shadow on the latter. Shadow 1 was illuminated by candle 2, and shadow 2 by only candle 1, whereas the remaining area was illuminated by both candles. He varied the distances of the candles until one of the shadows disappeared. This occurred when the relative distances of the two candles was about 8.16 to 1, or such that the intensities of illuminations (as given by the “inverse square law”) was about 1 to 66.67 (or 1.5 to 100). That is, the ratio of the brightness of the screen to that of the remaining shadow was 1.015.

Breton, P.

P. Breton, Comptes Rendus 105, 426–29 (1887).

Brodhun, E.

A. König and E. Brodhun, Experimentelle Untersuchungen über die Psychophtysiche Fundamentalform in Bezug auf den Gesichtssinn; Gesammelte Abhandl. z. Physiologischen Optik, p. 135–39. J. Blanchard, The Brightness Sensibility of the Retina, Phys. Rev. 11, 81–99 (1918); obtained results agreeing in general with König and Brodhun’s (and Aubert’s).
[CrossRef]

Cobb, P. W.

E. Q. Adams and P. W. Cobb, The Effect on Foveal Vision of Light (and Dark) Surroundings, V; J. Exper. Psychol. 5, 39–45 (1922).
[CrossRef]

P. W. Cobb and L. R. Geissler, The Effect on Foveal Vision of Bright Surroundings, I; Psychol. Rev. 20, 525–47 (1913). P. W. Cobb, The Effect on Foveal Vision of Bright Surroundings, II; Psychol. Rev. 21, 23–32 (1914). P. W. Cobb, The Effect on Foveal Vision of Bright Surroundings, III; J. Exper. Psychol. 1, 419–25 (1916); IV, J. Exper. Psychol. 1, 540–66 (1916).
[CrossRef]

Cooper, F. G.

F. G. Cooper, Munsell Manual of Color, on p. 33, Baltimore, 1929.

Delboeuf,

By way of comparison with the Plateau law, it can be shown that the Weber-Fechner law results from assuming that observers pick a mid-gray in such a way that it gives equal differences (rather than equal ratios) of sensations when compared with black and white; i.e., so that V2−Vm=Vm−V1. Delboeuf, Bull. de l’Acad. royale de Belgique 34, 250, 261 (1872), pointed out that according to the Weber-Fechner law, a small positive value of R corresponds to a negative value of V, and zero value of R to an infinitely negative value of V, which is an absurdity. Further, his results were not entirely independent of the illumination, as required by the Weber-Fechner law.

Ebbinghaus,

Ebbinghaus; Grundzuge der Psychologie, I, 497, Leipzig, 1902. W. Ament, Über das Verhaltnis der ebenmerklichen zu den ubernmerklichen Unterschieden bei Licht- und Schallintensitaten; Wundt’s Phil Stud. 16, 135–96 (1900).

Fröbes, J.

J. Fröbes, Ein Beitrag über die sogenannten Vergleichungen ubermerklicher Empfindungsunterschiede; Zeits. f. Psychologie 36, 304–80 (1904). A. Stefanini, Sulla legge di oscillazione dei diapsson e sulla misura dell’ intensita del suono; Atti della R. Acad. Lucchese 25, 305–400 (1889).

Geissler, L. R.

P. W. Cobb and L. R. Geissler, The Effect on Foveal Vision of Bright Surroundings, I; Psychol. Rev. 20, 525–47 (1913). P. W. Cobb, The Effect on Foveal Vision of Bright Surroundings, II; Psychol. Rev. 21, 23–32 (1914). P. W. Cobb, The Effect on Foveal Vision of Bright Surroundings, III; J. Exper. Psychol. 1, 419–25 (1916); IV, J. Exper. Psychol. 1, 540–66 (1916).
[CrossRef]

Keuffel, C. W.

C. W. Keuffel, A Direct Reading Spectrophotometer, J. Opt. Soc. Am. 11, 407 (1925); see the figure on p. 406.
[CrossRef]

König, A.

A. König and E. Brodhun, Experimentelle Untersuchungen über die Psychophtysiche Fundamentalform in Bezug auf den Gesichtssinn; Gesammelte Abhandl. z. Physiologischen Optik, p. 135–39. J. Blanchard, The Brightness Sensibility of the Retina, Phys. Rev. 11, 81–99 (1918); obtained results agreeing in general with König and Brodhun’s (and Aubert’s).
[CrossRef]

Lambert, J. H.

J. H. Lambert, Photometria, Augustae Videlic, 1760. C. A. Steinheil, Elemente der Helligkeitsmessungen am Sternhimmel; Abhandl. k. bayr. Akad. Wissensch., Math.-Phys. Cl. 2, 1 (1837). Arago, Oeuvres completes, Paris, X; 1858. G. T. Fechner, Über ein wichtiges psychophysisches Grundgesetz u. d. Beziehung z. Schatzung d. Sterngrossen, Abhandl. k. sachs. ges. Wissensch., Math.-phys. Kl. 4, 455 (1859). G. T. Fechner, Elemente der Psychophysik, Leipzig; 1860. The last-named obtained the Fechner fraction 0.010.

Lehman, A.

A. Lehman, Über die Anwendung der Methode der mittleren Abstufung auf den lichtsinn; Wundt’s Phil. Stud. 3, 497–533 (1886). H. Neiglick, Zur Psychophysik des Lichtsinns; Wundt’s Phil. Stud. 4, 28–111 (1888).

Masson, M. A.

M. A. Masson, Études de photometrie electrique; Ann. chim. et phys. [3] 14, 129 (1845). E. Kraepelin, Zur Frage der Gültigkeit des Weberschen Gesetzes bei Lichtempfindungen; Phil. Stud. 2, 306–26 (1885). E. Kraepelin, Nachtrag zu der Arbeit u. d. Gültigkeit des Weberschen Gesetzes bei Lichtempfindungen; Phil. Stud. 2, 651–57 (1885). Masson introduced the method of using a series of white disks each with a small black sector. When the disk was rotated a faint gray ring was seen on the white background. The size of the black sector giving a just perceptible gray ring furnished a determination of the Fechner fraction. Later experimenters modified this technique in various ways, in part for the purpose of eliminating certain contrast effects which might modify the results.

Merkel, J.

J. Merkel, Die Abhangigkeit zwischen Reiz und Empfindund, Wundt’s Phil. Stud. 4, 541 (1888); Wundt’s Phil. Stud. 5, 499 (1889); Wundt’s Phil. Stud. 10, 239 (1894).

Munsell, A. E. O.

A. E. O. Munsell and et al., Munsell Book of Color, on p. 46, Baltimore, 1929.

Munsell, A. H.

A. H. Munsell, Atlas of the Munsell Color System, Boston, 1915.

Plateau, J.

J. Plateau, Über die Messung physischer Empfindungen u. d. Gesetz welches die Starke d. erregenden Ursache verknupft, Pogg. Ann. 150, 465–76 (1873).

Priest, I. G.

I. G. Priest, The Spectral Distribution of Energy Required to Evoke the Gray Sensation, ; 1921. In the quotation, the word in brackets has been inserted by the authors.

Volkmann, A. W.

A. W. Volkmann, Physiol. Untersuchungen im Gebiete d. Optik 1, 56 (1863). H. Helmholtz, Handb. d. physiologischen Optik, Hamburg and Leipzig, 1886.

Ann. chim. et phys. [3] (1)

M. A. Masson, Études de photometrie electrique; Ann. chim. et phys. [3] 14, 129 (1845). E. Kraepelin, Zur Frage der Gültigkeit des Weberschen Gesetzes bei Lichtempfindungen; Phil. Stud. 2, 306–26 (1885). E. Kraepelin, Nachtrag zu der Arbeit u. d. Gültigkeit des Weberschen Gesetzes bei Lichtempfindungen; Phil. Stud. 2, 651–57 (1885). Masson introduced the method of using a series of white disks each with a small black sector. When the disk was rotated a faint gray ring was seen on the white background. The size of the black sector giving a just perceptible gray ring furnished a determination of the Fechner fraction. Later experimenters modified this technique in various ways, in part for the purpose of eliminating certain contrast effects which might modify the results.

Augustae Videlic (1)

J. H. Lambert, Photometria, Augustae Videlic, 1760. C. A. Steinheil, Elemente der Helligkeitsmessungen am Sternhimmel; Abhandl. k. bayr. Akad. Wissensch., Math.-Phys. Cl. 2, 1 (1837). Arago, Oeuvres completes, Paris, X; 1858. G. T. Fechner, Über ein wichtiges psychophysisches Grundgesetz u. d. Beziehung z. Schatzung d. Sterngrossen, Abhandl. k. sachs. ges. Wissensch., Math.-phys. Kl. 4, 455 (1859). G. T. Fechner, Elemente der Psychophysik, Leipzig; 1860. The last-named obtained the Fechner fraction 0.010.

Bull. de l’Acad. royale de Belgique (1)

By way of comparison with the Plateau law, it can be shown that the Weber-Fechner law results from assuming that observers pick a mid-gray in such a way that it gives equal differences (rather than equal ratios) of sensations when compared with black and white; i.e., so that V2−Vm=Vm−V1. Delboeuf, Bull. de l’Acad. royale de Belgique 34, 250, 261 (1872), pointed out that according to the Weber-Fechner law, a small positive value of R corresponds to a negative value of V, and zero value of R to an infinitely negative value of V, which is an absurdity. Further, his results were not entirely independent of the illumination, as required by the Weber-Fechner law.

Comptes Rendus (1)

P. Breton, Comptes Rendus 105, 426–29 (1887).

J. Exper. Psychol. (1)

E. Q. Adams and P. W. Cobb, The Effect on Foveal Vision of Light (and Dark) Surroundings, V; J. Exper. Psychol. 5, 39–45 (1922).
[CrossRef]

J. Opt. Soc. Am. (1)

C. W. Keuffel, A Direct Reading Spectrophotometer, J. Opt. Soc. Am. 11, 407 (1925); see the figure on p. 406.
[CrossRef]

Physiol. Untersuchungen im Gebiete d. Optik (1)

A. W. Volkmann, Physiol. Untersuchungen im Gebiete d. Optik 1, 56 (1863). H. Helmholtz, Handb. d. physiologischen Optik, Hamburg and Leipzig, 1886.

Physiologie der Netzhaut; (1)

H. Aubert, Physiologie der Netzhaut; pp. 52–82 (1865).

Pogg. Ann. (1)

J. Plateau, Über die Messung physischer Empfindungen u. d. Gesetz welches die Starke d. erregenden Ursache verknupft, Pogg. Ann. 150, 465–76 (1873).

Psychol. Rev. (1)

P. W. Cobb and L. R. Geissler, The Effect on Foveal Vision of Bright Surroundings, I; Psychol. Rev. 20, 525–47 (1913). P. W. Cobb, The Effect on Foveal Vision of Bright Surroundings, II; Psychol. Rev. 21, 23–32 (1914). P. W. Cobb, The Effect on Foveal Vision of Bright Surroundings, III; J. Exper. Psychol. 1, 419–25 (1916); IV, J. Exper. Psychol. 1, 540–66 (1916).
[CrossRef]

Wundt’s Phil. Stud. (2)

J. Merkel, Die Abhangigkeit zwischen Reiz und Empfindund, Wundt’s Phil. Stud. 4, 541 (1888); Wundt’s Phil. Stud. 5, 499 (1889); Wundt’s Phil. Stud. 10, 239 (1894).

A. Lehman, Über die Anwendung der Methode der mittleren Abstufung auf den lichtsinn; Wundt’s Phil. Stud. 3, 497–533 (1886). H. Neiglick, Zur Psychophysik des Lichtsinns; Wundt’s Phil. Stud. 4, 28–111 (1888).

Zeits. f. Psychologie (1)

J. Fröbes, Ein Beitrag über die sogenannten Vergleichungen ubermerklicher Empfindungsunterschiede; Zeits. f. Psychologie 36, 304–80 (1904). A. Stefanini, Sulla legge di oscillazione dei diapsson e sulla misura dell’ intensita del suono; Atti della R. Acad. Lucchese 25, 305–400 (1889).

Other (11)

A. König and E. Brodhun, Experimentelle Untersuchungen über die Psychophtysiche Fundamentalform in Bezug auf den Gesichtssinn; Gesammelte Abhandl. z. Physiologischen Optik, p. 135–39. J. Blanchard, The Brightness Sensibility of the Retina, Phys. Rev. 11, 81–99 (1918); obtained results agreeing in general with König and Brodhun’s (and Aubert’s).
[CrossRef]

Ebbinghaus; Grundzuge der Psychologie, I, 497, Leipzig, 1902. W. Ament, Über das Verhaltnis der ebenmerklichen zu den ubernmerklichen Unterschieden bei Licht- und Schallintensitaten; Wundt’s Phil Stud. 16, 135–96 (1900).

The relation between Value and Brilliance is as follows: “Brilliance is that attribute of any color in respect of which it may be classed as equivalent to some member of a series of grays ranging between black and white.” (Report of the Committee on Colorimetry of the Optical Society of America, J. O. S. A. and R. S. I.6, 534 (1922).) Value bears a relation to the color attribute brilliance similar to that which the Fahrenheit and Centigrade scales, as measured with the various (gas, mercury, etc.) types of thermometers, bear to temperature. Value is the practical approach to brilliance afforded by reflection standards, the special case of brilliance so represented having the important difference of corresponding to a constant level of adaptation of the eye. More precisely, value is the brilliance of the colors of a series of standards, varying in reflectance from zero to unity, in such a way that all visual intervals are uniform when viewed on a middle gray background by a light-adapted eye. The standard Munsell value unit is defined as one-tenth the difference in value between a surface of 0 percent reflectance and one of 100 percent reflectance when both are viewed on a background whose reflectance is about 18 percent and illuminated by 22.8 f.c. of daylight (5200°K).

A. E. O. Munsell and et al., Munsell Book of Color, on p. 46, Baltimore, 1929.

F. G. Cooper, Munsell Manual of Color, on p. 33, Baltimore, 1929.

A. H. Munsell, Atlas of the Munsell Color System, Boston, 1915.

The Ostwald scale is of the logarithmic type corresponding to the Weber-Fechner law, considered below; the “Atlas” value scale of A. H. Munsell is of the exponential type presaged by the work of Plateau and others (see below). A third type of law, that of Adams and Cobb considered below, has not been applied to practical value scales.

P. Bouguer, Traité d’optique sur la gradation de la lumiere, p. 51, Paris, (Lacaille)1760. He used the following method. He set up a post between two candles and a white cardboard so that each candle cast a shadow on the latter. Shadow 1 was illuminated by candle 2, and shadow 2 by only candle 1, whereas the remaining area was illuminated by both candles. He varied the distances of the candles until one of the shadows disappeared. This occurred when the relative distances of the two candles was about 8.16 to 1, or such that the intensities of illuminations (as given by the “inverse square law”) was about 1 to 66.67 (or 1.5 to 100). That is, the ratio of the brightness of the screen to that of the remaining shadow was 1.015.

The strengths of the correcting spheres or cylinders worn by four of the five observers were equal to or less than one diopter. The glasses worn by C. E. B. were O. D. −2.5 sph., −3 cyl. axis 165, O. S. −4.25 sph., −2 cyl. axis 10.

This photometer operated on the “cat’s-eye” principle, that is, the area of the variable aperture through which a reflecting standard was illuminated with decreasing intensity until the sample was matched (or the movement of the brightness indicator) was proportional to the square of the diagonal of the (square) aperture. Equal areas of aperture or equal movements of the indicator corresponded approximately to equal sensation (rather than equal reflection) differences. This relation corresponded further to the simple rule: The percentage reflectance of any one of the ten steps of value in the Munsell “Atlas Value Scale” is obtained by multiplying this value by itself. For example, value 7 gives 7×7 or 49 percent. This earlier Munsell value scale was carefully examined by the U. S. Bureau of Standards, with the results reported by Priest, Gibson and McNicholas (Bur. Stand. Tech. Pap. No. 167, p. 27; 1920) as follows:Value level1/2/3/4/5/6/7/8/9/Value×value149162536496481%B. S. findings249162334466072%Considering the drawbacks of the photometer resulting from its portable construction, the results are very satisfactory.

I. G. Priest, The Spectral Distribution of Energy Required to Evoke the Gray Sensation, ; 1921. In the quotation, the word in brackets has been inserted by the authors.

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Figures (13)

Fig. 1
Fig. 1

Showing variation of the Fechner fraction with logarithm of brightness.

Fig. 2
Fig. 2

Apparatus for J.N.D. experiments at low brightnesses.

Fig. 3
Fig. 3

Showing limitation of field of view by blue glasses. Broken curve with cardboard screen; unbroken curve, without cardboard screen.

Fig. 4
Fig. 4

Apparatus for J.N.D. experiments at high brightnesses.

Fig. 5
Fig. 5

Showing disks in position behind aperture.

Fig. 7
Fig. 7

Variation of Fechner fraction ΔB/B with brightness B; natural pupil, light adaptation, light surrounding field (4.69 ml).

Fig. 8
Fig. 8

Showing the number of J.N.D. units corresponding to each reflectance or brightness. Observer L.L.S.

Fig. 9
Fig. 9

Showing variation of ΔR with R 1 2. Curve used in obtaining by interpolation additional data on corresponding amounts of ΔR and R.

Fig. 10
Fig. 10

Showing the relation between value and reflectance, value and brightness, for each of 6 observers.

Fig. 11
Fig. 11

Apparatus used in determining value scales by the method of value steps. Only one of the nine movable strips (S5) is shown in this figure.

Fig. 12
Fig. 12

Comparison of average value scales obtained by the just-noticeable-difference and value-step methods. Gray background, light adaptation.

Fig. 13
Fig. 13

Showing mean variation of individual value scales from the average.

Tables (10)

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Table I Showing the smallest change in reflectance obtainable with pairs of rotating disks.

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Table II Just noticeable differences at five levels of reflectance.(Data given in both reflectance and brightness units. A reflectance of 100 percent corresponds to a brightness of 24.5 ml.)

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Table III Showing variation of Fechner fraction (ΔB/B) with logarithm of brightness (log B) in light adaptation. (B expressed in ml.)

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Table IV Number of just-noticeable-difference units between various intervals of reflectance for observer L.L.S.Data from area measurements on 1/ΔR, R Curve.

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Table V Showing series of reflectances dividing area under curve into ten equal parts. Observer L.L.S.

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Table VI Data used in plotting curve shown in Fig. 9.Observer L.L.S.

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Table VII Total number of just-noticeable-difference units between 0 and 24.5 ml. (0 and 100 percent reflectance.)

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Table VIII Six individual value scales. Showing series of reflectances corresponding to equal value intervals between 0 and 100 percent reflectance. Natural pupil, light adaptations, light surrounding field (19.1 percent), intensity of illumination 22.8 f.c.

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Table IX Showing series of reflectances selected by each of sixteen observers to form evenly graded scales of values.

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Table X Showing the mean variations of individual value scales from the average value scales.

Equations (4)

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V = c log R + k ,
V = k R c ,
V = c log [ ( R + k ) / k ] ,
V = c R / ( R + R a ) ,