Abstract

The bril scale, obtained from extensive experimental data by Hanes, represents an attempt to establish a subjective scale of brightness by the determination of particular luminances which produce specific ratios of brightness. This scale, like other scales obtained from fractionation data, necessarily assumes a one-to-one correspondence between intensity of stimulus and magnitude of response—an assumption in conflict with known facts regarding adaptation.

It is shown that the reformulation of the Fechner law proposed several years ago, aided by results obtained from rating-scale techniques, can predict quantitatively all of the data used for the construction of the bril scale. Since this theoretical treatment takes explicit account of adaptation, it follows that each of the ratios determined by fractionation techniques has meaning by itself, but that the combination of these ratios into a scale of wide range is not justified. The fallacy involved in such combination is the assumption that a given stimulus is psychologically equivalent to itself when it is presented under different conditions, and, therefore, under different states of adaptation.

© 1954 Optical Society of America

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References

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  1. R. M. Hanes, J. Exptl. Psychol. 39, 719 (1949).
    [Crossref]
  2. W. C. Michels and H. Helson, Am. J. Psychol. 62, 355 (1949).
    [Crossref] [PubMed]
  3. E.g., see M. C. Nash, Am. J. Psychol. 63, 214 (1950).
    [Crossref] [PubMed]
  4. Helson, Michels, and Sturgeon, Am. J. Psychol. (to be published).
  5. W. C. Michels and H. Helson, Am. J. Psychol. (to be published).
  6. W. C. Michels and H. Helson, Am. J. Psychol. (to be published).
  7. See reference 4. The judgment constant C is related to the least count l.c. on the response scale by the relation. l.c.=N/C.
  8. R. M. Hanes, J. Exptl. Psychol. 39, 726 (1949).
  9. Adeline Scovil, unpublished data (private communication).
  10. R. M. Hanes, J. Exptl. Psychol. 39, 721 (1949).

1950 (1)

E.g., see M. C. Nash, Am. J. Psychol. 63, 214 (1950).
[Crossref] [PubMed]

1949 (4)

R. M. Hanes, J. Exptl. Psychol. 39, 726 (1949).

R. M. Hanes, J. Exptl. Psychol. 39, 721 (1949).

R. M. Hanes, J. Exptl. Psychol. 39, 719 (1949).
[Crossref]

W. C. Michels and H. Helson, Am. J. Psychol. 62, 355 (1949).
[Crossref] [PubMed]

Hanes, R. M.

R. M. Hanes, J. Exptl. Psychol. 39, 719 (1949).
[Crossref]

R. M. Hanes, J. Exptl. Psychol. 39, 726 (1949).

R. M. Hanes, J. Exptl. Psychol. 39, 721 (1949).

Helson,

Helson, Michels, and Sturgeon, Am. J. Psychol. (to be published).

Helson, H.

W. C. Michels and H. Helson, Am. J. Psychol. 62, 355 (1949).
[Crossref] [PubMed]

W. C. Michels and H. Helson, Am. J. Psychol. (to be published).

W. C. Michels and H. Helson, Am. J. Psychol. (to be published).

Michels,

Helson, Michels, and Sturgeon, Am. J. Psychol. (to be published).

Michels, W. C.

W. C. Michels and H. Helson, Am. J. Psychol. 62, 355 (1949).
[Crossref] [PubMed]

W. C. Michels and H. Helson, Am. J. Psychol. (to be published).

W. C. Michels and H. Helson, Am. J. Psychol. (to be published).

Nash, M. C.

E.g., see M. C. Nash, Am. J. Psychol. 63, 214 (1950).
[Crossref] [PubMed]

Scovil, Adeline

Adeline Scovil, unpublished data (private communication).

Sturgeon,

Helson, Michels, and Sturgeon, Am. J. Psychol. (to be published).

Am. J. Psychol. (2)

W. C. Michels and H. Helson, Am. J. Psychol. 62, 355 (1949).
[Crossref] [PubMed]

E.g., see M. C. Nash, Am. J. Psychol. 63, 214 (1950).
[Crossref] [PubMed]

J. Exptl. Psychol. (3)

R. M. Hanes, J. Exptl. Psychol. 39, 726 (1949).

R. M. Hanes, J. Exptl. Psychol. 39, 719 (1949).
[Crossref]

R. M. Hanes, J. Exptl. Psychol. 39, 721 (1949).

Other (5)

Adeline Scovil, unpublished data (private communication).

Helson, Michels, and Sturgeon, Am. J. Psychol. (to be published).

W. C. Michels and H. Helson, Am. J. Psychol. (to be published).

W. C. Michels and H. Helson, Am. J. Psychol. (to be published).

See reference 4. The judgment constant C is related to the least count l.c. on the response scale by the relation. l.c.=N/C.

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Figures (2)

Fig. 1
Fig. 1

Luminances judged to yield brightnesses which are fixed multiples of the brightness of a given standard. The center cross marks on the vertical bars represent the mean luminances judged to be n times as bright as the standard, according to Hanes, and the lengths of the bars indicate the standard deviations of these means. The solid lines are plots of the predicted luminances, according to the reformulated Fechner law.

Fig. 2
Fig. 2

Dependence of the self-adaptation coefficient on the angle subtended by the source. The solid line shows mean values as obtained by Scovil; the dashed lines indicate the limits of the estimated uncertainties in these values.

Equations (16)

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B = const L 0.38 ,
B = B 0 + K log e ( L / A ) ,
J = N + K log e ( L / A ) ,
K = - 1 / log e ( 1 - 1 / N ) ,
log A = p log L + q log Q + r log R .
log A = p log L + ( 1 - p ) log A .
J = N + K log e ( L / A ) ,
K = ( 1 - p ) K .
log A c = s log S + ( 1 - s ) log A ,
J c = N + K log e ( L / A c ) ,
B 1 = N + K log e ( S / A c ) .
B n = n B 1 = N + K log e ( L / A c ) .
log e ( L / S ) = ( n - 1 ) { N / K + log e ( S / A c ) } .
log e L - log e A c > N / K
log e ( L / S ) = ( 1 - 1 / n ) { N / K + log e ( L / A c ) } .
N / K = - N log e ( 1 - 1 / N ) / ( 1 - p ) .