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References

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  1. T. C. Porter, Proc. R. S.,  70, 313–329, 1902.
    [CrossRef]
  2. Ives, Phil. Mag., Sept., 1912, p. 352.
    [CrossRef]
  3. Allen, Phil. Mag., July, 1919, p. 82.
  4. Ives and Kingsbury, Phil. Mag., April, 1916, p. 290.
    [CrossRef]
  5. Made and calibrated by the Eastman Kodak Co.
  6. Wratten monochromatic filter for isolating blue mercury lines.
  7. The constant 2 is introduced in order to have an expression in terms of the range of fluctuation, according to the diffusion theory.
  8. The points shown for discs B1 and C1, in Fig. 4 which were not included in the main series, are extrapolated from the A1 and D1 values by utilizing the well determined ratio previously obtained.
  9. The use of this factor, which is called for by the “diffusion” theory (see ref. 4) leads to formulae in which the first periodic term figures as a square. Actually, due to the short frequency range in which all the observations fall, the formulae involving the square fit the data nearly as well as (7). They demand, however, in order to fit, a value of δ of about .001. This is so far below the very large values of the Fechner fraction which hold at low intensities as to force the conclusion that the diffusion theory must be modified if it is to cover this illumination region.

1919 (1)

Allen, Phil. Mag., July, 1919, p. 82.

1916 (1)

Ives and Kingsbury, Phil. Mag., April, 1916, p. 290.
[CrossRef]

1912 (1)

Ives, Phil. Mag., Sept., 1912, p. 352.
[CrossRef]

1902 (1)

T. C. Porter, Proc. R. S.,  70, 313–329, 1902.
[CrossRef]

Allen,

Allen, Phil. Mag., July, 1919, p. 82.

Ives,

Ives and Kingsbury, Phil. Mag., April, 1916, p. 290.
[CrossRef]

Ives, Phil. Mag., Sept., 1912, p. 352.
[CrossRef]

Kingsbury,

Ives and Kingsbury, Phil. Mag., April, 1916, p. 290.
[CrossRef]

Porter, T. C.

T. C. Porter, Proc. R. S.,  70, 313–329, 1902.
[CrossRef]

Phil. Mag. (3)

Ives, Phil. Mag., Sept., 1912, p. 352.
[CrossRef]

Allen, Phil. Mag., July, 1919, p. 82.

Ives and Kingsbury, Phil. Mag., April, 1916, p. 290.
[CrossRef]

Proc. R. S. (1)

T. C. Porter, Proc. R. S.,  70, 313–329, 1902.
[CrossRef]

Other (5)

Made and calibrated by the Eastman Kodak Co.

Wratten monochromatic filter for isolating blue mercury lines.

The constant 2 is introduced in order to have an expression in terms of the range of fluctuation, according to the diffusion theory.

The points shown for discs B1 and C1, in Fig. 4 which were not included in the main series, are extrapolated from the A1 and D1 values by utilizing the well determined ratio previously obtained.

The use of this factor, which is called for by the “diffusion” theory (see ref. 4) leads to formulae in which the first periodic term figures as a square. Actually, due to the short frequency range in which all the observations fall, the formulae involving the square fit the data nearly as well as (7). They demand, however, in order to fit, a value of δ of about .001. This is so far below the very large values of the Fechner fraction which hold at low intensities as to force the conclusion that the diffusion theory must be modified if it is to cover this illumination region.

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Figures (4)

Fig. 1
Fig. 1

Apparatus used for study of low intensity flicker phenomena

Fig. 2
Fig. 2

Sector discs used to control the wave-form of the stimulus

Fig. 3
Fig. 3

Critical frequency—log brightness determinations for various wave-forms, showing wedge scale value necessary to insure observations falling in rod vision region

Fig. 4
Fig. 4

Critical frequency against amplitude (left) and against opening (right). Full lines plotted from empirical formula.

Tables (1)

Tables Icon

Table 1 Critical Speed in Cycles per Second

Equations (20)

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I t = I 2 + I α sin ω t
I t = I 2 . + 8 I α π 2 ( sin ω t - 1 9 sin 3 ω t + 1 25 sin 5 ω t - )
I t = I 2 ± 2 I α π ( sin ω t + 1 2 sin 2 ω t + 1 3 sin 3 ω t + )
I t = I a v + 4 I α π ( sin π ϕ cos ω t + 1 2 sin 2 π ϕ cos 2 ω t + . . )
I t = I ϕ + 2 I π ( sin π ϕ cos ω t + 1 2 sin 2 π ϕ cos 2 ω t + . . )
I t = I 2 + 4 I α π ( cos ω t + 1 3 cos 3 ω t + 1 5 cos 5 ω t + )
2 × coefficient of 1 st periodic term constant term = W
ω = c log 2 W δ
for the A discs             ω = c log ( 16 α ) ( π δ )
for the B discs             ω = c log ( 8 α ) ( π δ )
for the C discs             ω = c log ( 32 α ) ( π 2 δ )
for the D discs             ω = c log ( 4 α ) ( δ )
for the E discs             ω = c log ( 4 sin π ϕ ) ( π ϕ δ )
I 2 + I α sin ω t
the reaction             I 2 + I α e - ω c sin ( ω t - ω c )
2 I α e - ω c
2 I α e - ω c I 2 = 4 α e - ω c
4 α e - ω c = δ
or             ω = c log 4 α δ = c log 2 W δ
ω = c log 2 W δ