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  1. H. v. Helmholtz, Physiol. Optik, second edition, 444–458; Zeit. f. Psych. Physiol. Sinnesorgane 2, 1–30; Zeit. f. Psych. Physiol. Sinnesorgane 3, 1–20, 517 (1891); Akad. der Wiss. Berlin1071–1083 (1891); Wiss. Abhandlungen3, 407–475 (Leipzig, 1895). Erwin Schrödinger, Ann. d. Physik 63, 481–520 (1920). Ludwik Silberstein, J. Opt. Soc. Am. 28, 62–85 (1938).
    [Crossref]
  2. H. Laurens and W. F. Hamilton, Am. J. Physiol. 65, 547 (1923). W. D. Wright and F. H. G. Pitt, Proc. Phys. Soc. 46, 459–468 (1934). W. D. Wright, Proc. Phys. Soc. 53, 96 (1941).The last paper indicates that a tenfold increase of luminance may decrease the discrimination step fifty percent. G. Haase, Ann. d. Physik 20, 75–105 (1934), reported a considerable dependence of wave-length discrimination on luminance. His results for Δλ vs. λ differ seriously, however, from the results of Wright and Pitt and the reliability of his method may therefore be questioned.
    [Crossref]
  3. Hecht, Peskin, and Patt, in J. Gen. Physiol. 22, 7–19 (1938), showed that this is approximately true for cone vision, i.e., for luminance much greater than 0.01 foot-lambert. They reported for blue, green, yellow, orange, and red “a maximum variation of about ten per cent from the mean, which is probably of no importance.” They showed that the assumption is certainly not correct for rod vision, i.e., for luminance much less than 0.01 foot-lambert.
  4. No experimental tests of this assumption have been reported. Although it is implicit in most guesses about the way in which sub-liminal differences of luminance and chromaticity are compounded, this assumption has not previously been stated explicitly. It is not easy to devise an experimental procedure adequate for testing this assumption. The ultimate test may have to be indirect, a verification of predictions based on this and better established hypotheses.
  5. L. C. Martin, F. L. Warburton, and W. J. Morgan, (H. M. Stationery Office, London, 1933). D. L. MacAdam, J. Opt. Soc. Am. 32, 247–274 (1942). L. Silberstein and D. L. MacAdam, ibid.  35, 32–39 (1945).
    [Crossref]
  6. Parry Moon and D. E. Spencer, J. Opt. Soc. Am. 33, 260–269 (1943). G. A. Fry, J. Opt. Soc. Am. 35, 114–135 (1945).
    [Crossref]
  7. D. L. MacAdam, J. Opt. Soc. Am. 33, 675–679 (1943); J. Frank. Inst. 238, 195–210 (1944); J. Opt. Soc. Am. 35, 616–617 (1945). A. W. Wundheiler, J. Opt. Soc. Am. 35, 767–771 (1945).
    [Crossref]

1943 (2)

1938 (1)

Hecht, Peskin, and Patt, in J. Gen. Physiol. 22, 7–19 (1938), showed that this is approximately true for cone vision, i.e., for luminance much greater than 0.01 foot-lambert. They reported for blue, green, yellow, orange, and red “a maximum variation of about ten per cent from the mean, which is probably of no importance.” They showed that the assumption is certainly not correct for rod vision, i.e., for luminance much less than 0.01 foot-lambert.

1923 (1)

H. Laurens and W. F. Hamilton, Am. J. Physiol. 65, 547 (1923). W. D. Wright and F. H. G. Pitt, Proc. Phys. Soc. 46, 459–468 (1934). W. D. Wright, Proc. Phys. Soc. 53, 96 (1941).The last paper indicates that a tenfold increase of luminance may decrease the discrimination step fifty percent. G. Haase, Ann. d. Physik 20, 75–105 (1934), reported a considerable dependence of wave-length discrimination on luminance. His results for Δλ vs. λ differ seriously, however, from the results of Wright and Pitt and the reliability of his method may therefore be questioned.
[Crossref]

Hamilton, W. F.

H. Laurens and W. F. Hamilton, Am. J. Physiol. 65, 547 (1923). W. D. Wright and F. H. G. Pitt, Proc. Phys. Soc. 46, 459–468 (1934). W. D. Wright, Proc. Phys. Soc. 53, 96 (1941).The last paper indicates that a tenfold increase of luminance may decrease the discrimination step fifty percent. G. Haase, Ann. d. Physik 20, 75–105 (1934), reported a considerable dependence of wave-length discrimination on luminance. His results for Δλ vs. λ differ seriously, however, from the results of Wright and Pitt and the reliability of his method may therefore be questioned.
[Crossref]

Hecht,

Hecht, Peskin, and Patt, in J. Gen. Physiol. 22, 7–19 (1938), showed that this is approximately true for cone vision, i.e., for luminance much greater than 0.01 foot-lambert. They reported for blue, green, yellow, orange, and red “a maximum variation of about ten per cent from the mean, which is probably of no importance.” They showed that the assumption is certainly not correct for rod vision, i.e., for luminance much less than 0.01 foot-lambert.

Helmholtz, H. v.

H. v. Helmholtz, Physiol. Optik, second edition, 444–458; Zeit. f. Psych. Physiol. Sinnesorgane 2, 1–30; Zeit. f. Psych. Physiol. Sinnesorgane 3, 1–20, 517 (1891); Akad. der Wiss. Berlin1071–1083 (1891); Wiss. Abhandlungen3, 407–475 (Leipzig, 1895). Erwin Schrödinger, Ann. d. Physik 63, 481–520 (1920). Ludwik Silberstein, J. Opt. Soc. Am. 28, 62–85 (1938).
[Crossref]

Laurens, H.

H. Laurens and W. F. Hamilton, Am. J. Physiol. 65, 547 (1923). W. D. Wright and F. H. G. Pitt, Proc. Phys. Soc. 46, 459–468 (1934). W. D. Wright, Proc. Phys. Soc. 53, 96 (1941).The last paper indicates that a tenfold increase of luminance may decrease the discrimination step fifty percent. G. Haase, Ann. d. Physik 20, 75–105 (1934), reported a considerable dependence of wave-length discrimination on luminance. His results for Δλ vs. λ differ seriously, however, from the results of Wright and Pitt and the reliability of his method may therefore be questioned.
[Crossref]

MacAdam, D. L.

Martin, L. C.

L. C. Martin, F. L. Warburton, and W. J. Morgan, (H. M. Stationery Office, London, 1933). D. L. MacAdam, J. Opt. Soc. Am. 32, 247–274 (1942). L. Silberstein and D. L. MacAdam, ibid.  35, 32–39 (1945).
[Crossref]

Moon, Parry

Morgan, W. J.

L. C. Martin, F. L. Warburton, and W. J. Morgan, (H. M. Stationery Office, London, 1933). D. L. MacAdam, J. Opt. Soc. Am. 32, 247–274 (1942). L. Silberstein and D. L. MacAdam, ibid.  35, 32–39 (1945).
[Crossref]

Patt,

Hecht, Peskin, and Patt, in J. Gen. Physiol. 22, 7–19 (1938), showed that this is approximately true for cone vision, i.e., for luminance much greater than 0.01 foot-lambert. They reported for blue, green, yellow, orange, and red “a maximum variation of about ten per cent from the mean, which is probably of no importance.” They showed that the assumption is certainly not correct for rod vision, i.e., for luminance much less than 0.01 foot-lambert.

Peskin,

Hecht, Peskin, and Patt, in J. Gen. Physiol. 22, 7–19 (1938), showed that this is approximately true for cone vision, i.e., for luminance much greater than 0.01 foot-lambert. They reported for blue, green, yellow, orange, and red “a maximum variation of about ten per cent from the mean, which is probably of no importance.” They showed that the assumption is certainly not correct for rod vision, i.e., for luminance much less than 0.01 foot-lambert.

Spencer, D. E.

Warburton, F. L.

L. C. Martin, F. L. Warburton, and W. J. Morgan, (H. M. Stationery Office, London, 1933). D. L. MacAdam, J. Opt. Soc. Am. 32, 247–274 (1942). L. Silberstein and D. L. MacAdam, ibid.  35, 32–39 (1945).
[Crossref]

Am. J. Physiol. (1)

H. Laurens and W. F. Hamilton, Am. J. Physiol. 65, 547 (1923). W. D. Wright and F. H. G. Pitt, Proc. Phys. Soc. 46, 459–468 (1934). W. D. Wright, Proc. Phys. Soc. 53, 96 (1941).The last paper indicates that a tenfold increase of luminance may decrease the discrimination step fifty percent. G. Haase, Ann. d. Physik 20, 75–105 (1934), reported a considerable dependence of wave-length discrimination on luminance. His results for Δλ vs. λ differ seriously, however, from the results of Wright and Pitt and the reliability of his method may therefore be questioned.
[Crossref]

J. Gen. Physiol. (1)

Hecht, Peskin, and Patt, in J. Gen. Physiol. 22, 7–19 (1938), showed that this is approximately true for cone vision, i.e., for luminance much greater than 0.01 foot-lambert. They reported for blue, green, yellow, orange, and red “a maximum variation of about ten per cent from the mean, which is probably of no importance.” They showed that the assumption is certainly not correct for rod vision, i.e., for luminance much less than 0.01 foot-lambert.

J. Opt. Soc. Am. (2)

Other (3)

H. v. Helmholtz, Physiol. Optik, second edition, 444–458; Zeit. f. Psych. Physiol. Sinnesorgane 2, 1–30; Zeit. f. Psych. Physiol. Sinnesorgane 3, 1–20, 517 (1891); Akad. der Wiss. Berlin1071–1083 (1891); Wiss. Abhandlungen3, 407–475 (Leipzig, 1895). Erwin Schrödinger, Ann. d. Physik 63, 481–520 (1920). Ludwik Silberstein, J. Opt. Soc. Am. 28, 62–85 (1938).
[Crossref]

No experimental tests of this assumption have been reported. Although it is implicit in most guesses about the way in which sub-liminal differences of luminance and chromaticity are compounded, this assumption has not previously been stated explicitly. It is not easy to devise an experimental procedure adequate for testing this assumption. The ultimate test may have to be indirect, a verification of predictions based on this and better established hypotheses.

L. C. Martin, F. L. Warburton, and W. J. Morgan, (H. M. Stationery Office, London, 1933). D. L. MacAdam, J. Opt. Soc. Am. 32, 247–274 (1942). L. Silberstein and D. L. MacAdam, ibid.  35, 32–39 (1945).
[Crossref]

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Equations (11)

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u ¯ = u ¯ + w ¯ u / y , υ ¯ = υ ¯ + w ¯ υ / y , y ¯ = w ¯
A u ¯ 2 + 2 B u ¯ υ ¯ + C υ ¯ 2 + e w ¯ 2 = 1 ,
A ( u ¯ y ) 2 + 2 B ( u ¯ y ) ( υ ¯ y ) + C ( υ ¯ y ) 2 = 1.
a ( u ¯ y u y ¯ y 2 ) 2 + 2 b ( u ¯ y u y ¯ y 2 ) ( υ ¯ y υ y ¯ y 2 ) + c ( υ ¯ y υ y ¯ y 2 ) 2 + e y ¯ 2 = 1.
d s 2 = a [ d ( u / y ) ] 2 + 2 b d ( u / y ) d ( υ / y ) + c [ d ( υ / y ) ] 2 + e d y 2 .
ξ = u / y , η = υ / y ,
d s 2 = a ( ξ , η ) d ξ 2 + 2 b ( ξ , η ) d ξ d η + c ( ξ , η ) d η 2 + e ( y ) d y 2 ,
a Δ ξ 2 + 2 b Δ ξ Δ η + c Δ η 2 + e Δ y 2 = 1
Δ u = ξ y ξ y , Δ υ = η y η y ,
y Δ u u Δ y = ξ y y ξ y 2 ( ξ y y ξ y 2 ) = Δ ξ y y , etc .
a Δ ξ 2 + 2 b Δ ξ Δ η + c Δ η 2 + ( e Δ y 2 1 ) ( y / y ) 2 = 0.