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  1. S. P. Langley, “The bolometer and radiant energy,” Proc. Am. Acad. 16, 342 (1881).
    [CrossRef]
  2. S. P. Langley, “Energy and vision,” Phil. Mag. [5] 27, 1 (1889).
    [CrossRef]
  3. In addition to Langley, these are:(a)G. Grijns and A. K. Noyons, “Ueber die absolute Empfindlichkeit des Auges für Licht,” Arch. Anat. und Physiol.25 (1905);(b)H. Zwaardemaker, “Die physiologisch wahrehmbaren Energiewanderungen,” Ergeb. Physiol. 4, 423 (1905);(c)J. von Kries and J. A. E. Eyster, “Über die zur Erregung des Sehorgans erforderlichen Energiemenzen,” Zeits. Sinnesphysiol. 41, 394 (1907);(d)H. E. Ives, “The minimum radiation visually perceptible,” Astrophys. J. 44, 124 (1916);(e)H. N. Russell, “The minimum radiation visually perceptible,” Astrophys. J. 45, 60 (1917);(f)P. Reeves, “The minimum radiation visually perceptible,” Astrophys. J. 46, 167 (1917);(g)H. Buisson, “The minimum radiation visually perceptible,” Astrophys. J. 46, 296 (1917);(h)P. Lecomte du Noüy, “Energy and vision,” J. Gen. Physiol. 3, 743 (1921);(i)J. Chariton and C. A. Lea, “Some experiments concerning the counting of scintillations produced by alpha particles. Part I,” Proc. Roy. Soc. A122, 304 (1929);(j)H. A. Wentworth, “A quantitative study of achromatic and chromatic sensitivity from center to periphery of the visual field,” Psych. Monograph 50, 189 pp. (1930);(k)R. B. Barnes and M. Czerny, “Lässt sich ein Schroteffekt der Photonen mit dem Auge beobachten?” Zeits. f. Physik 79, 436 (1932).
    [CrossRef]
  4. A. C. Hardy and F. H. Perrin, The Principles of Optics (McGraw-Hill, New York, 1932).
  5. H. Piper, “Über Dunkeladaptation,” Zeits. Psychol. u. Physiol. Sinnesorgane 31, 161 (1903);S. Hecht, C. Haig, and A. M. Chase, “The influence of light adaptation on subsequent dark adaptation of the eye,” J. Gen. Physiol.,  20, 831 (1937).
  6. G. Østerberg, “Topography of the layer of rods and cones in the human retina,” Acta Ophth., Copenhagen, Supplement 6, pp. 106 (1935).
  7. H. A. Wentworth, see footnote 3 (j).
  8. For a summary of the field see G. Wald, “Area and visual threshold,” J. Gen. Physiol. 21, 269 (1938).
  9. C. H. Graham and R. Margaria, “Area and the intensity-time relation in the peripheral retina,” Am. J. Physiol. 113, 299 (1935).
  10. S. Hecht and R. E. Williams, “The visibility of monochromatic radiation and the absorption spectrum of visual purple,” J. Gen. Physiol. 5, 1 (1922).
  11. C. Roggenbau and A. Wetthauer, “Über die Durchlässigkeit der brechenden Augenmedien für langwelliges Licht nach Untersuchungen am Rindsauge,” Klin. Monatsbl. Augenheilk. 79, 456 (1927).
  12. E. Ludvigh and E. F. McCarthy, “Absorption of visible light by the refractive media of the human eye,” Arch. Ophthal. 20, 37 (1938).
    [CrossRef]
  13. A. Koenig, “Üeber den menschlichen Sehpurpur und seine Bedeuting für das Sehen,” Sitzungsb. Akad. Wissensch., Berlin, 577 (1894).
  14. G. Wald, “On rhodopsin in solution,” J. Gen. Physiol. 21, 795 (1938).
  15. A. M. Chase and C. Haig, “The absorption spectrum of visual purple,” J. Gen. Physiol. 21, 411 (1938).
  16. R. J. Lythgoe, “The absorption spectra of visual purple and of indicator yellow,” J. Physiol. 89, 331 (1937).
  17. H. J. A. Dartnall and C. F. Goodeve, “Scotopic luminosity curve and the absorption spectrum of visual purple,” Nature 139, 409 (1937).
    [CrossRef]
  18. H. J. A. Dartnall, C. F. Goodeve, and R. J. Lythgoe, “The effect of temperature on the photochemical bleaching of visual purple solutions,” Proc. Roy. Soc. A164, 216 (1938).
    [CrossRef]
  19. T. C. Fry, Probability and its Engineering Uses, (Van Nostrand, New York, 1928).
  20. J. P. Guilford, Psychometric Methods (McGraw-Hill, New York, 1936).

1938 (5)

For a summary of the field see G. Wald, “Area and visual threshold,” J. Gen. Physiol. 21, 269 (1938).

E. Ludvigh and E. F. McCarthy, “Absorption of visible light by the refractive media of the human eye,” Arch. Ophthal. 20, 37 (1938).
[CrossRef]

G. Wald, “On rhodopsin in solution,” J. Gen. Physiol. 21, 795 (1938).

A. M. Chase and C. Haig, “The absorption spectrum of visual purple,” J. Gen. Physiol. 21, 411 (1938).

H. J. A. Dartnall, C. F. Goodeve, and R. J. Lythgoe, “The effect of temperature on the photochemical bleaching of visual purple solutions,” Proc. Roy. Soc. A164, 216 (1938).
[CrossRef]

1937 (2)

R. J. Lythgoe, “The absorption spectra of visual purple and of indicator yellow,” J. Physiol. 89, 331 (1937).

H. J. A. Dartnall and C. F. Goodeve, “Scotopic luminosity curve and the absorption spectrum of visual purple,” Nature 139, 409 (1937).
[CrossRef]

1935 (2)

C. H. Graham and R. Margaria, “Area and the intensity-time relation in the peripheral retina,” Am. J. Physiol. 113, 299 (1935).

G. Østerberg, “Topography of the layer of rods and cones in the human retina,” Acta Ophth., Copenhagen, Supplement 6, pp. 106 (1935).

1927 (1)

C. Roggenbau and A. Wetthauer, “Über die Durchlässigkeit der brechenden Augenmedien für langwelliges Licht nach Untersuchungen am Rindsauge,” Klin. Monatsbl. Augenheilk. 79, 456 (1927).

1922 (1)

S. Hecht and R. E. Williams, “The visibility of monochromatic radiation and the absorption spectrum of visual purple,” J. Gen. Physiol. 5, 1 (1922).

1905 (1)

In addition to Langley, these are:(a)G. Grijns and A. K. Noyons, “Ueber die absolute Empfindlichkeit des Auges für Licht,” Arch. Anat. und Physiol.25 (1905);(b)H. Zwaardemaker, “Die physiologisch wahrehmbaren Energiewanderungen,” Ergeb. Physiol. 4, 423 (1905);(c)J. von Kries and J. A. E. Eyster, “Über die zur Erregung des Sehorgans erforderlichen Energiemenzen,” Zeits. Sinnesphysiol. 41, 394 (1907);(d)H. E. Ives, “The minimum radiation visually perceptible,” Astrophys. J. 44, 124 (1916);(e)H. N. Russell, “The minimum radiation visually perceptible,” Astrophys. J. 45, 60 (1917);(f)P. Reeves, “The minimum radiation visually perceptible,” Astrophys. J. 46, 167 (1917);(g)H. Buisson, “The minimum radiation visually perceptible,” Astrophys. J. 46, 296 (1917);(h)P. Lecomte du Noüy, “Energy and vision,” J. Gen. Physiol. 3, 743 (1921);(i)J. Chariton and C. A. Lea, “Some experiments concerning the counting of scintillations produced by alpha particles. Part I,” Proc. Roy. Soc. A122, 304 (1929);(j)H. A. Wentworth, “A quantitative study of achromatic and chromatic sensitivity from center to periphery of the visual field,” Psych. Monograph 50, 189 pp. (1930);(k)R. B. Barnes and M. Czerny, “Lässt sich ein Schroteffekt der Photonen mit dem Auge beobachten?” Zeits. f. Physik 79, 436 (1932).
[CrossRef]

1903 (1)

H. Piper, “Über Dunkeladaptation,” Zeits. Psychol. u. Physiol. Sinnesorgane 31, 161 (1903);S. Hecht, C. Haig, and A. M. Chase, “The influence of light adaptation on subsequent dark adaptation of the eye,” J. Gen. Physiol.,  20, 831 (1937).

1889 (1)

S. P. Langley, “Energy and vision,” Phil. Mag. [5] 27, 1 (1889).
[CrossRef]

1881 (1)

S. P. Langley, “The bolometer and radiant energy,” Proc. Am. Acad. 16, 342 (1881).
[CrossRef]

Chase, A. M.

A. M. Chase and C. Haig, “The absorption spectrum of visual purple,” J. Gen. Physiol. 21, 411 (1938).

Dartnall, H. J. A.

H. J. A. Dartnall, C. F. Goodeve, and R. J. Lythgoe, “The effect of temperature on the photochemical bleaching of visual purple solutions,” Proc. Roy. Soc. A164, 216 (1938).
[CrossRef]

H. J. A. Dartnall and C. F. Goodeve, “Scotopic luminosity curve and the absorption spectrum of visual purple,” Nature 139, 409 (1937).
[CrossRef]

Fry, T. C.

T. C. Fry, Probability and its Engineering Uses, (Van Nostrand, New York, 1928).

Goodeve, C. F.

H. J. A. Dartnall, C. F. Goodeve, and R. J. Lythgoe, “The effect of temperature on the photochemical bleaching of visual purple solutions,” Proc. Roy. Soc. A164, 216 (1938).
[CrossRef]

H. J. A. Dartnall and C. F. Goodeve, “Scotopic luminosity curve and the absorption spectrum of visual purple,” Nature 139, 409 (1937).
[CrossRef]

Graham, C. H.

C. H. Graham and R. Margaria, “Area and the intensity-time relation in the peripheral retina,” Am. J. Physiol. 113, 299 (1935).

Grijns, G.

In addition to Langley, these are:(a)G. Grijns and A. K. Noyons, “Ueber die absolute Empfindlichkeit des Auges für Licht,” Arch. Anat. und Physiol.25 (1905);(b)H. Zwaardemaker, “Die physiologisch wahrehmbaren Energiewanderungen,” Ergeb. Physiol. 4, 423 (1905);(c)J. von Kries and J. A. E. Eyster, “Über die zur Erregung des Sehorgans erforderlichen Energiemenzen,” Zeits. Sinnesphysiol. 41, 394 (1907);(d)H. E. Ives, “The minimum radiation visually perceptible,” Astrophys. J. 44, 124 (1916);(e)H. N. Russell, “The minimum radiation visually perceptible,” Astrophys. J. 45, 60 (1917);(f)P. Reeves, “The minimum radiation visually perceptible,” Astrophys. J. 46, 167 (1917);(g)H. Buisson, “The minimum radiation visually perceptible,” Astrophys. J. 46, 296 (1917);(h)P. Lecomte du Noüy, “Energy and vision,” J. Gen. Physiol. 3, 743 (1921);(i)J. Chariton and C. A. Lea, “Some experiments concerning the counting of scintillations produced by alpha particles. Part I,” Proc. Roy. Soc. A122, 304 (1929);(j)H. A. Wentworth, “A quantitative study of achromatic and chromatic sensitivity from center to periphery of the visual field,” Psych. Monograph 50, 189 pp. (1930);(k)R. B. Barnes and M. Czerny, “Lässt sich ein Schroteffekt der Photonen mit dem Auge beobachten?” Zeits. f. Physik 79, 436 (1932).
[CrossRef]

Guilford, J. P.

J. P. Guilford, Psychometric Methods (McGraw-Hill, New York, 1936).

Haig, C.

A. M. Chase and C. Haig, “The absorption spectrum of visual purple,” J. Gen. Physiol. 21, 411 (1938).

Hardy, A. C.

A. C. Hardy and F. H. Perrin, The Principles of Optics (McGraw-Hill, New York, 1932).

Hecht, S.

S. Hecht and R. E. Williams, “The visibility of monochromatic radiation and the absorption spectrum of visual purple,” J. Gen. Physiol. 5, 1 (1922).

Koenig, A.

A. Koenig, “Üeber den menschlichen Sehpurpur und seine Bedeuting für das Sehen,” Sitzungsb. Akad. Wissensch., Berlin, 577 (1894).

Langley, S. P.

S. P. Langley, “Energy and vision,” Phil. Mag. [5] 27, 1 (1889).
[CrossRef]

S. P. Langley, “The bolometer and radiant energy,” Proc. Am. Acad. 16, 342 (1881).
[CrossRef]

Ludvigh, E.

E. Ludvigh and E. F. McCarthy, “Absorption of visible light by the refractive media of the human eye,” Arch. Ophthal. 20, 37 (1938).
[CrossRef]

Lythgoe, R. J.

H. J. A. Dartnall, C. F. Goodeve, and R. J. Lythgoe, “The effect of temperature on the photochemical bleaching of visual purple solutions,” Proc. Roy. Soc. A164, 216 (1938).
[CrossRef]

R. J. Lythgoe, “The absorption spectra of visual purple and of indicator yellow,” J. Physiol. 89, 331 (1937).

Margaria, R.

C. H. Graham and R. Margaria, “Area and the intensity-time relation in the peripheral retina,” Am. J. Physiol. 113, 299 (1935).

McCarthy, E. F.

E. Ludvigh and E. F. McCarthy, “Absorption of visible light by the refractive media of the human eye,” Arch. Ophthal. 20, 37 (1938).
[CrossRef]

Noyons, A. K.

In addition to Langley, these are:(a)G. Grijns and A. K. Noyons, “Ueber die absolute Empfindlichkeit des Auges für Licht,” Arch. Anat. und Physiol.25 (1905);(b)H. Zwaardemaker, “Die physiologisch wahrehmbaren Energiewanderungen,” Ergeb. Physiol. 4, 423 (1905);(c)J. von Kries and J. A. E. Eyster, “Über die zur Erregung des Sehorgans erforderlichen Energiemenzen,” Zeits. Sinnesphysiol. 41, 394 (1907);(d)H. E. Ives, “The minimum radiation visually perceptible,” Astrophys. J. 44, 124 (1916);(e)H. N. Russell, “The minimum radiation visually perceptible,” Astrophys. J. 45, 60 (1917);(f)P. Reeves, “The minimum radiation visually perceptible,” Astrophys. J. 46, 167 (1917);(g)H. Buisson, “The minimum radiation visually perceptible,” Astrophys. J. 46, 296 (1917);(h)P. Lecomte du Noüy, “Energy and vision,” J. Gen. Physiol. 3, 743 (1921);(i)J. Chariton and C. A. Lea, “Some experiments concerning the counting of scintillations produced by alpha particles. Part I,” Proc. Roy. Soc. A122, 304 (1929);(j)H. A. Wentworth, “A quantitative study of achromatic and chromatic sensitivity from center to periphery of the visual field,” Psych. Monograph 50, 189 pp. (1930);(k)R. B. Barnes and M. Czerny, “Lässt sich ein Schroteffekt der Photonen mit dem Auge beobachten?” Zeits. f. Physik 79, 436 (1932).
[CrossRef]

Østerberg, G.

G. Østerberg, “Topography of the layer of rods and cones in the human retina,” Acta Ophth., Copenhagen, Supplement 6, pp. 106 (1935).

Perrin, F. H.

A. C. Hardy and F. H. Perrin, The Principles of Optics (McGraw-Hill, New York, 1932).

Piper, H.

H. Piper, “Über Dunkeladaptation,” Zeits. Psychol. u. Physiol. Sinnesorgane 31, 161 (1903);S. Hecht, C. Haig, and A. M. Chase, “The influence of light adaptation on subsequent dark adaptation of the eye,” J. Gen. Physiol.,  20, 831 (1937).

Roggenbau, C.

C. Roggenbau and A. Wetthauer, “Über die Durchlässigkeit der brechenden Augenmedien für langwelliges Licht nach Untersuchungen am Rindsauge,” Klin. Monatsbl. Augenheilk. 79, 456 (1927).

Wald, G.

For a summary of the field see G. Wald, “Area and visual threshold,” J. Gen. Physiol. 21, 269 (1938).

G. Wald, “On rhodopsin in solution,” J. Gen. Physiol. 21, 795 (1938).

Wentworth, H. A.

H. A. Wentworth, see footnote 3 (j).

Wetthauer, A.

C. Roggenbau and A. Wetthauer, “Über die Durchlässigkeit der brechenden Augenmedien für langwelliges Licht nach Untersuchungen am Rindsauge,” Klin. Monatsbl. Augenheilk. 79, 456 (1927).

Williams, R. E.

S. Hecht and R. E. Williams, “The visibility of monochromatic radiation and the absorption spectrum of visual purple,” J. Gen. Physiol. 5, 1 (1922).

Acta Ophth., Copenhagen (1)

G. Østerberg, “Topography of the layer of rods and cones in the human retina,” Acta Ophth., Copenhagen, Supplement 6, pp. 106 (1935).

Am. J. Physiol. (1)

C. H. Graham and R. Margaria, “Area and the intensity-time relation in the peripheral retina,” Am. J. Physiol. 113, 299 (1935).

Arch. Anat. und Physiol. (1)

In addition to Langley, these are:(a)G. Grijns and A. K. Noyons, “Ueber die absolute Empfindlichkeit des Auges für Licht,” Arch. Anat. und Physiol.25 (1905);(b)H. Zwaardemaker, “Die physiologisch wahrehmbaren Energiewanderungen,” Ergeb. Physiol. 4, 423 (1905);(c)J. von Kries and J. A. E. Eyster, “Über die zur Erregung des Sehorgans erforderlichen Energiemenzen,” Zeits. Sinnesphysiol. 41, 394 (1907);(d)H. E. Ives, “The minimum radiation visually perceptible,” Astrophys. J. 44, 124 (1916);(e)H. N. Russell, “The minimum radiation visually perceptible,” Astrophys. J. 45, 60 (1917);(f)P. Reeves, “The minimum radiation visually perceptible,” Astrophys. J. 46, 167 (1917);(g)H. Buisson, “The minimum radiation visually perceptible,” Astrophys. J. 46, 296 (1917);(h)P. Lecomte du Noüy, “Energy and vision,” J. Gen. Physiol. 3, 743 (1921);(i)J. Chariton and C. A. Lea, “Some experiments concerning the counting of scintillations produced by alpha particles. Part I,” Proc. Roy. Soc. A122, 304 (1929);(j)H. A. Wentworth, “A quantitative study of achromatic and chromatic sensitivity from center to periphery of the visual field,” Psych. Monograph 50, 189 pp. (1930);(k)R. B. Barnes and M. Czerny, “Lässt sich ein Schroteffekt der Photonen mit dem Auge beobachten?” Zeits. f. Physik 79, 436 (1932).
[CrossRef]

Arch. Ophthal. (1)

E. Ludvigh and E. F. McCarthy, “Absorption of visible light by the refractive media of the human eye,” Arch. Ophthal. 20, 37 (1938).
[CrossRef]

J. Gen. Physiol. (4)

S. Hecht and R. E. Williams, “The visibility of monochromatic radiation and the absorption spectrum of visual purple,” J. Gen. Physiol. 5, 1 (1922).

G. Wald, “On rhodopsin in solution,” J. Gen. Physiol. 21, 795 (1938).

A. M. Chase and C. Haig, “The absorption spectrum of visual purple,” J. Gen. Physiol. 21, 411 (1938).

For a summary of the field see G. Wald, “Area and visual threshold,” J. Gen. Physiol. 21, 269 (1938).

J. Physiol. (1)

R. J. Lythgoe, “The absorption spectra of visual purple and of indicator yellow,” J. Physiol. 89, 331 (1937).

Klin. Monatsbl. Augenheilk. (1)

C. Roggenbau and A. Wetthauer, “Über die Durchlässigkeit der brechenden Augenmedien für langwelliges Licht nach Untersuchungen am Rindsauge,” Klin. Monatsbl. Augenheilk. 79, 456 (1927).

Nature (1)

H. J. A. Dartnall and C. F. Goodeve, “Scotopic luminosity curve and the absorption spectrum of visual purple,” Nature 139, 409 (1937).
[CrossRef]

Phil. Mag. [5] (1)

S. P. Langley, “Energy and vision,” Phil. Mag. [5] 27, 1 (1889).
[CrossRef]

Proc. Am. Acad. (1)

S. P. Langley, “The bolometer and radiant energy,” Proc. Am. Acad. 16, 342 (1881).
[CrossRef]

Proc. Roy. Soc. (1)

H. J. A. Dartnall, C. F. Goodeve, and R. J. Lythgoe, “The effect of temperature on the photochemical bleaching of visual purple solutions,” Proc. Roy. Soc. A164, 216 (1938).
[CrossRef]

Zeits. Psychol. u. Physiol. Sinnesorgane (1)

H. Piper, “Über Dunkeladaptation,” Zeits. Psychol. u. Physiol. Sinnesorgane 31, 161 (1903);S. Hecht, C. Haig, and A. M. Chase, “The influence of light adaptation on subsequent dark adaptation of the eye,” J. Gen. Physiol.,  20, 831 (1937).

Other (5)

H. A. Wentworth, see footnote 3 (j).

A. C. Hardy and F. H. Perrin, The Principles of Optics (McGraw-Hill, New York, 1932).

T. C. Fry, Probability and its Engineering Uses, (Van Nostrand, New York, 1928).

J. P. Guilford, Psychometric Methods (McGraw-Hill, New York, 1936).

A. Koenig, “Üeber den menschlichen Sehpurpur und seine Bedeuting für das Sehen,” Sitzungsb. Akad. Wissensch., Berlin, 577 (1894).

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Figures (6)

F. 1
F. 1

Optical system for measuring minimum energies necessary for vision. The eye at the pupil P fixates the red point FP and observes the test field formed by the lens FL and the diaphragm D. The light for this field comes from the lamp L through the neutral filter F and wedge W, through the double monochromator M1M2 and is controlled by the shutter S.

F. 2
F. 2

Absorption spectrum of frog’s visual purple. The data from the three sources have been made equal at 500 mμ.

F. 3
F. 3

Percentage absorption spectra of various concentrations of visual purple. For convenience in comparing the shapes of the curves, their maxima have all been equated to 1 and are thus superimposed at 500 mμ. The actual fraction absorbed at the maximum is shown for each curve. It is apparent that with increasing concentration the absorption curve steadily increases in width.

F. 4
F. 4

Comparison of scotopic luminosity at the retina with visual purple absorption. The points are the data of Hecht and Williams corrected for quantum effectiveness and ocular media transmission. The curves are the percentage absorption spectra of visual purple; the upper curve represents 20 percent maximal absorption, and the lower one 5 percent maximal absorption. All curves have been made equal to 1 at the maximum, 500 mμ, for ease in comparison.

F. 5
F. 5

Poisson probability distributions. For any average number of quanta per flash, the ordinates give the probabilities that the flash will deliver to the retina n or more quanta, depending on the value assumed for n.

F. 6
F. 6

Relation between the average energy content of a flash of light and the frequency with which it is seen by three observers. Each point represents 50 flashes. The curves are the Poisson distributions of Fig. 5 for n values of 5, 6, and 7.

Equations (1)

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P n = a n e a / n !