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  1. Parry Moon and D. E. Spencer, J. Opt. Soc. Am. 33, 89 (1943).
    [Crossref]
  2. Commission Internationale de l’Eclairage, 1931 Session, Compte Rendu (Cambridge University Press, 1932), p. 25.
  3. Karl Pearson, Phil. Trans. Roy. Soc. A197, 446 (1901).
  4. J. Peters, Zehnstellige Logarithmen, (Berlin, 1922), Vol. I, Table 6. T. C. Fry, Probability and its Engineering Uses, (D. Van Nostrand Company, New York, 1928), p. 429.
  5. R. T. Birge, Rev. Mod. Phys. 13, 233 (1941).
    [Crossref]
  6. G. K. Burgess, Bur. Stand. J. Research 1, 635 (1928); RP22.
    [Crossref]
  7. J. F. Skogland, Nat. Bur. Stand. Misc. Pub. 86 (1929).
  8. Parry Moon, Scientific Basis of Illuminating Engineering (McGraw-Hill Book Company, Inc., New York, 1936), p. 135, Fig. 5.16.
  9. H. E. Ives, J. Opt. Soc. Am. 12, 75 (1926).
    [Crossref]
  10. H. T. Wensel, Bur. Stand. J. Research 22, 375 (1939); RP1189. “Illuminating engineering nomenclature and photometric standards,” Illum. Eng. 36, 815 (1941).
  11. Roeser, Caldwell, and Wensel, Bur. Stand. J. Research 6, 1119 (1931); RP326.
    [Crossref]
  12. Wensel, Roeser, Barbrow, and Caldwell, Bur. Stand. J. Research 6, 1103 (1931); RP325.
    [Crossref]
  13. Proceedings of the International Committee on Illumination, Tenth Session, 1939, p. 93.
  14. Approximate because of the possible effect of y¯B(λ) or y¯c(λ) and because the Wien function is employed instead of the Planck function.
  15. Reference 2. The original specification calls for 2848°K for C2=14350, which corresponds to 2842°K for C2=14320 as used in this paper.
  16. J. Guild, Trans. Opt. Soc. London,  32, 1 (1930).
    [Crossref]
  17. A. C. Hardy, J. Opt. Soc. Am. 25, 305 (1935); J. L. Michaelson, J. Opt. Soc. Am. 28, 365 (1938).
    [Crossref]
  18. Dorothy Nickerson, J. Opt. Soc. Am. 29, 1 (1939); Trans. I. E. S.,  34, 1233 (1939); and Trans. I. E. S.,  36, 373 (1941).
    [Crossref]
  19. Bowditch and Null, J. Opt. Soc. Am. 28, 500 (1938).
    [Crossref]
  20. O. Steindler, Sitz. Akad. Wiss. Wien,  115, 39 (1906). Eight other investigators obtain the same order of magnitude. See D. B. Judd, , Fig. 2.
  21. R. S. Hunter, J. Opt. Soc. Am. 32, 509 (1942), see particularly p. 517, Fig. 2.
    [Crossref]
  22. Committee on Colorimetry, J. Opt. Soc. Am. 34, 633 (1944).
  23. D. L. MacAdam, J. Opt. Soc. Am. 32, 247 (1942).
    [Crossref]
  24. Reference 23, p. 262.
  25. W. D. Wright, Trans. Opt. Soc. London,  30, 141 (1928); (1929).
    [Crossref]
  26. J. Guild, Phil. Trans. Roy. Soc. A230, 149 (1931).
  27. T. Smith and J. Guild, Trans. Dept. Soc., London 33, 73 (1931).
    [Crossref]

1944 (1)

1943 (1)

1942 (2)

1941 (1)

R. T. Birge, Rev. Mod. Phys. 13, 233 (1941).
[Crossref]

1939 (2)

H. T. Wensel, Bur. Stand. J. Research 22, 375 (1939); RP1189. “Illuminating engineering nomenclature and photometric standards,” Illum. Eng. 36, 815 (1941).

Dorothy Nickerson, J. Opt. Soc. Am. 29, 1 (1939); Trans. I. E. S.,  34, 1233 (1939); and Trans. I. E. S.,  36, 373 (1941).
[Crossref]

1938 (1)

1935 (1)

1931 (4)

Roeser, Caldwell, and Wensel, Bur. Stand. J. Research 6, 1119 (1931); RP326.
[Crossref]

Wensel, Roeser, Barbrow, and Caldwell, Bur. Stand. J. Research 6, 1103 (1931); RP325.
[Crossref]

J. Guild, Phil. Trans. Roy. Soc. A230, 149 (1931).

T. Smith and J. Guild, Trans. Dept. Soc., London 33, 73 (1931).
[Crossref]

1930 (1)

J. Guild, Trans. Opt. Soc. London,  32, 1 (1930).
[Crossref]

1929 (1)

J. F. Skogland, Nat. Bur. Stand. Misc. Pub. 86 (1929).

1928 (2)

W. D. Wright, Trans. Opt. Soc. London,  30, 141 (1928); (1929).
[Crossref]

G. K. Burgess, Bur. Stand. J. Research 1, 635 (1928); RP22.
[Crossref]

1926 (1)

1906 (1)

O. Steindler, Sitz. Akad. Wiss. Wien,  115, 39 (1906). Eight other investigators obtain the same order of magnitude. See D. B. Judd, , Fig. 2.

1901 (1)

Karl Pearson, Phil. Trans. Roy. Soc. A197, 446 (1901).

Barbrow,

Wensel, Roeser, Barbrow, and Caldwell, Bur. Stand. J. Research 6, 1103 (1931); RP325.
[Crossref]

Birge, R. T.

R. T. Birge, Rev. Mod. Phys. 13, 233 (1941).
[Crossref]

Bowditch,

Burgess, G. K.

G. K. Burgess, Bur. Stand. J. Research 1, 635 (1928); RP22.
[Crossref]

Caldwell,

Wensel, Roeser, Barbrow, and Caldwell, Bur. Stand. J. Research 6, 1103 (1931); RP325.
[Crossref]

Roeser, Caldwell, and Wensel, Bur. Stand. J. Research 6, 1119 (1931); RP326.
[Crossref]

Guild, J.

J. Guild, Phil. Trans. Roy. Soc. A230, 149 (1931).

T. Smith and J. Guild, Trans. Dept. Soc., London 33, 73 (1931).
[Crossref]

J. Guild, Trans. Opt. Soc. London,  32, 1 (1930).
[Crossref]

Hardy, A. C.

Hunter, R. S.

Ives, H. E.

MacAdam, D. L.

Moon, Parry

Parry Moon and D. E. Spencer, J. Opt. Soc. Am. 33, 89 (1943).
[Crossref]

Parry Moon, Scientific Basis of Illuminating Engineering (McGraw-Hill Book Company, Inc., New York, 1936), p. 135, Fig. 5.16.

Nickerson, Dorothy

Null,

Pearson, Karl

Karl Pearson, Phil. Trans. Roy. Soc. A197, 446 (1901).

Peters, J.

J. Peters, Zehnstellige Logarithmen, (Berlin, 1922), Vol. I, Table 6. T. C. Fry, Probability and its Engineering Uses, (D. Van Nostrand Company, New York, 1928), p. 429.

Roeser,

Roeser, Caldwell, and Wensel, Bur. Stand. J. Research 6, 1119 (1931); RP326.
[Crossref]

Wensel, Roeser, Barbrow, and Caldwell, Bur. Stand. J. Research 6, 1103 (1931); RP325.
[Crossref]

Skogland, J. F.

J. F. Skogland, Nat. Bur. Stand. Misc. Pub. 86 (1929).

Smith, T.

T. Smith and J. Guild, Trans. Dept. Soc., London 33, 73 (1931).
[Crossref]

Spencer, D. E.

Steindler, O.

O. Steindler, Sitz. Akad. Wiss. Wien,  115, 39 (1906). Eight other investigators obtain the same order of magnitude. See D. B. Judd, , Fig. 2.

Wensel,

Roeser, Caldwell, and Wensel, Bur. Stand. J. Research 6, 1119 (1931); RP326.
[Crossref]

Wensel, Roeser, Barbrow, and Caldwell, Bur. Stand. J. Research 6, 1103 (1931); RP325.
[Crossref]

Wensel, H. T.

H. T. Wensel, Bur. Stand. J. Research 22, 375 (1939); RP1189. “Illuminating engineering nomenclature and photometric standards,” Illum. Eng. 36, 815 (1941).

Wright, W. D.

W. D. Wright, Trans. Opt. Soc. London,  30, 141 (1928); (1929).
[Crossref]

Bur. Stand. J. Research (4)

G. K. Burgess, Bur. Stand. J. Research 1, 635 (1928); RP22.
[Crossref]

H. T. Wensel, Bur. Stand. J. Research 22, 375 (1939); RP1189. “Illuminating engineering nomenclature and photometric standards,” Illum. Eng. 36, 815 (1941).

Roeser, Caldwell, and Wensel, Bur. Stand. J. Research 6, 1119 (1931); RP326.
[Crossref]

Wensel, Roeser, Barbrow, and Caldwell, Bur. Stand. J. Research 6, 1103 (1931); RP325.
[Crossref]

J. Opt. Soc. Am. (8)

Nat. Bur. Stand. Misc. Pub. (1)

J. F. Skogland, Nat. Bur. Stand. Misc. Pub. 86 (1929).

Phil. Trans. Roy. Soc. (2)

Karl Pearson, Phil. Trans. Roy. Soc. A197, 446 (1901).

J. Guild, Phil. Trans. Roy. Soc. A230, 149 (1931).

Rev. Mod. Phys. (1)

R. T. Birge, Rev. Mod. Phys. 13, 233 (1941).
[Crossref]

Sitz. Akad. Wiss. Wien (1)

O. Steindler, Sitz. Akad. Wiss. Wien,  115, 39 (1906). Eight other investigators obtain the same order of magnitude. See D. B. Judd, , Fig. 2.

Trans. Dept. Soc., London (1)

T. Smith and J. Guild, Trans. Dept. Soc., London 33, 73 (1931).
[Crossref]

Trans. Opt. Soc. London (2)

J. Guild, Trans. Opt. Soc. London,  32, 1 (1930).
[Crossref]

W. D. Wright, Trans. Opt. Soc. London,  30, 141 (1928); (1929).
[Crossref]

Other (7)

Reference 23, p. 262.

Proceedings of the International Committee on Illumination, Tenth Session, 1939, p. 93.

Approximate because of the possible effect of y¯B(λ) or y¯c(λ) and because the Wien function is employed instead of the Planck function.

Reference 2. The original specification calls for 2848°K for C2=14350, which corresponds to 2842°K for C2=14320 as used in this paper.

Parry Moon, Scientific Basis of Illuminating Engineering (McGraw-Hill Book Company, Inc., New York, 1936), p. 135, Fig. 5.16.

J. Peters, Zehnstellige Logarithmen, (Berlin, 1922), Vol. I, Table 6. T. C. Fry, Probability and its Engineering Uses, (D. Van Nostrand Company, New York, 1928), p. 429.

Commission Internationale de l’Eclairage, 1931 Session, Compte Rendu (Cambridge University Press, 1932), p. 25.

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Figures (10)

Fig. 1
Fig. 1

Calculated curves for x ¯ , y ¯, and z ¯.

Fig. 2
Fig. 2

Comparison of calculated and C. I. E. values for z ¯. Curve is calculated, points are C. I. E. results.

Fig. 3
Fig. 3

Comparison of calculated and C. I. E. values for x ¯.

Fig. 4
Fig. 4

Comparison of calculated and C. I. E. values for y ¯.

Fig. 5
Fig. 5

Comparison of YA and YD for Planckian radiation. Logarithmic scales are used along both axes. The correction term, YD is seen to reach a value of approximately one-tenth YA at the lowest temperatures, but over most of the temperature range it is less than one-hundredth of YA.

Fig. 6
Fig. 6

Comparison of the components of X for Planckian radiation. At low temperatures XA and XB are approximately equal; and since they are used with opposite signs, XXc. At high temperatures, Xc is still the largest of the 3 components but XA is also fairly large.

Fig. 7
Fig. 7

Efficacy of Planckian radiation in affecting the eye. Y/Dr is luminous efficacy in youngs per watt. X/Dr and Z/Dr are corresponding quantities based on the other two trichromatic weighting functions.

Fig. 8
Fig. 8

Chromaticity diagram. ○ Standard C. I. E. values: ● Analytic approximation.

Fig. 9
Fig. 9

MacAdam ellipse giving standard deviation (in the chromaticity diagram) for a single color match. The center of the ellipse represents 3500°K Planckian radiation in the C.I.E. chromaticity diagram. The small circle represents the analytic approximation of the same radiation. The data for the ellipse are taken from MacAdam’s Fig. 36.

Fig. 10
Fig. 10

MacAdam ellipse. Planckian radiation, 7000°K. Ellipse data from MacAdam’s Fig. 35. Small circle represents the analytic approximation. (See Table XXII.)

Tables (24)

Tables Icon

Table I Values of the constants in Eq. (1).

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Table II Wave-length range in which one or two terms can be neglected.

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Table III Values of the x ¯(λ) components.

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Table IV Values of y ¯(λ) at long wave-lengths.

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Table V The function y ¯(λ).

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Table VI Calculated values of x ¯(λ), y ¯(λ), and z ¯(λ).

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Table VII The gamma-function.

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Table VIII Difference between y ¯ A(λ) and y ¯(λ).

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Table IX Relative size of the correction term.

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Table X Schedule for integration.

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Table XI Equal-energy spectrum (m=0).

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Table XII Blackbody radiation, a comparison of the Planck and Wien equations.

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Table XIII Calculation for Planckian radiation, T=14000°K.

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Table XIV Planckian radiation.

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Table XV Location of maxima of w(λ) J(λ).

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Table XVI Spectral distributions for Planckian radiators suggested for standard illuminants.

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Table XVII Spectral locus.

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Table XVIII Planckian locus.

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Table XIX Comparison of integrated values.

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Table XX Comparison of spectral loci.

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Table XXI Discrepancies in the spectral locus (long wave-lengths).

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Table XXII Chromaticity of Planckian radiation. (C2=14320).

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Table XXIII Comparison of calculated chromaticities.

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Table XXIV Comparison of chromaticity data.

Equations (120)

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w ( λ ) = ( A / λ p ) exp ( - q / λ ) ,
z ¯ ( λ ) = ( A / λ p ) exp ( - q / λ ) ,
x ¯ ( λ ) = x ¯ A ( λ ) - x ¯ B ( λ ) + x ¯ C ( λ ) .
x ¯ A ( λ ) = z ¯ ( λ ) / 4.5700.
x ¯ B ( λ ) = ( A / λ p ) exp ( - q / λ ) ,
x ¯ C ( λ ) = ( A / λ p ) exp ( - q / λ ) .
y ¯ ( λ ) = y ¯ A ( λ ) ,             λ 0.620 μ .
y ¯ ( λ ) = y ¯ A ( λ ) - y ¯ B ( λ ) ,             0.620 λ 0.670.
y ¯ ( λ ) = y ¯ C ( λ ) ,             λ 0.670.
y ¯ A ( λ ) = ( A / λ p ) exp ( - q / λ ) .
y ¯ B ( λ ) = ( A / λ p ) exp ( - q / λ ) .
y ¯ C ( λ ) = 0.36678             137 x ¯ C ( λ ) .
log z ¯ ( λ ) = 398.09140 - 365.33880 log * λ - 71.63713             53666 / λ ,
log x ¯ B ( λ ) = 554.51150 - 500.00000 log * λ - 103.14493             94520 / λ ,
log x ¯ C ( λ ) = 405.63330 - 336.03850 log * λ - 86.47037             65371 / λ ,
log y ¯ A ( λ ) = 214.60430 - 182.19050 log * λ - 43.83638             21199 / λ ,
log y ¯ B ( λ ) = 8.23360 - 10 - 3.20500 log * ( λ - 0.620 ) - 0.055676             55259 / ( λ - 0.620 ) ,
L = 0 w ( λ ) J ( λ ) d λ ,
X = 0 x ¯ ( λ ) J ( λ ) d λ , Y = 0 y ¯ ( λ ) J ( λ ) d λ , Z = 0 z ¯ ( λ ) J ( λ ) d λ .
J ( λ ) = m = 0 K m λ m ,
J ( λ ) = m = - B m exp ( i m / λ ) ,
J ( λ ) = ( C 1 / λ 5 ) [ 1 / ( exp ( C 2 / λ T ) - 1 ] .
0 x r exp ( - a x ) d x = Γ ( r + 1 ) a r + 1 ,
Γ ( x ) = ( 2 π ) 1 2 ( x - 1 ) x - 1 2 exp [ - ( x - 1 ) ] · [ 1 + 1 / ( 12 ( x - 1 ) ) + 1 / ( 288 ( x - 1 ) 2 ) + ]
log Γ ( x ) = 0.39908             993 + ( x - 1 2 ) log ( x - 1 ) - 0.4342945 ( x - 1 ) + log [ 1 + 1 / ( 12 ( x - 1 ) ) + 1 / ( 288 ( x - 1 ) 2 ) + ] .
Γ ( x + 1 ) = x Γ ( x ) ,
log Γ ( x + 1 ) = log Γ ( x ) + log x ,
log Γ ( x - 1 ) = log Γ ( x ) - log ( x - 1 ) .
L = A K 0 exp ( - q / λ ) λ p d λ = A K 0 x p - 2 exp ( - q x ) d x = A K Γ ( p - 1 ) q p - 1 .
log L = log A + log K + log Γ ( p - 1 ) - ( p - 1 ) log q .
L = A K m 0 exp ( - q / λ ) λ p - m d λ = A K m Γ ( p - m - 1 ) q p - m - 1 ,
log L = log A + log K m + log Γ ( p - m - 1 ) - ( p - m - 1 ) log q .
( L / K ) m = A [ Γ ( p - m - 1 ) / q p - m - 1 ] .
( L / K ) m + 1 = A [ Γ ( p - m - 2 ) / q p - m - 2 ] .
( L / K ) m + 1 / ( L / K ) m = Γ ( p - m - 2 ) / Γ ( p - m - 1 ) · q p - m - 1 / q p - m - 2 ,
( L / K ) m + 1 = ( L / K ) m · q / ( p - m - 2 ) .
( L / K ) m - 1 = ( L / K ) m · ( p - m - 1 ) / q .
L = A B m 0 exp [ - 1 λ ( q - i m ) ] λ p d λ = A B m Γ ( p - 1 ) ( q - i m ) p - 1 .
exp ( i m / λ ) = cos ( m / λ ) + i sin ( m / λ ) .
L = A Γ ( p - 1 ) · R [ B m ( q - i m ) - ( p - 1 ) ] .
L = A Γ ( p - 1 ) · J [ B m ( q - i m ) - ( p - 1 ) ] .
J ( λ ) = ( C 1 / λ 5 ) exp ( - n C 2 λ T ) .
L = A C 1 0 exp [ - 1 λ ( q + n C 2 / λ T ) ] λ p + 5 d λ = A C 1 Γ ( p + 4 ) ( q + n C 2 / T ) p + 4
log L = log A + log C 1 + log Γ ( p + 4 ) - ( p + 4 ) log ( q + n C 2 / T ) .
L n + 1 = L n [ q + n C 2 / T q + ( n + 1 ) C 2 / T ] p + 4 ,
L n - 1 = L n [ q + n C 2 / T q + ( n - 1 ) C 2 / T ] p + 4 .
J ( λ ) = C 1 λ 5 1 exp ( C 2 / λ T ) - 1 = ( C 1 T / C 2 λ 4 ) [ 1 + y / ( 2 ) ! + y 2 / ( 3 ) ! + ] - 1 ,
J ( λ ) = C 1 T C 2 λ 4 [ 1 - 1 2 C 2 λ T + 1 12 ( C 2 λ T ) 2 - 1 720 ( C 2 λ T ) 4 + ] .
J ( λ ) = C 1 T / C 2 λ 4 ,
L = A C 1 T C 2 [ Γ ( p + 3 ) q p + 3 - 1 2 ( C 2 T ) Γ ( p + 4 ) q p + 4 + 1 12 ( C 2 T ) 2 Γ ( p + 5 ) q p + 5 - 1 720 ( C 2 T ) 4 Γ ( p + 7 ) q p + 7 + ] = A C 1 T C 2 Γ ( p + 3 ) q p + 3 [ 1 - 1 2 ( C 2 T ) ( p + 4 ) q + 1 12 ( C 2 T ) 2 ( p + 4 ) ( p + 5 ) q 2 - 1 720 ( C 2 T ) × ( p + 4 ) ( p + 5 ) ( p + 6 ) ( p + 7 ) q 4 + ] .
L = ( A C 1 T / C 2 ) ( Γ ( p + 3 ) / q p + 3 ) .
J ( λ ) = ( C 1 / λ 5 ) exp ( - n C 2 / λ T ) ,
ρ ( λ ) = K m λ m .
ρ ( λ ) J ( λ ) = ( C 1 K m / λ 5 - m ) exp ( - n C 2 / λ T ) .
L = A C 1 K m 0 exp [ - 1 λ ( q + n C 2 / T ) ] λ p + 5 - m d λ = A C 1 K m Γ ( p + 4 - m ) ( q + n C 2 / T ) p + 4 - m ,
log L = log A + log C 1 + log K m + log Γ ( p + 4 - m ) - ( p + 4 - m ) log ( q + n C 2 / T ) .
( L / K ) m + 1 = ( L / K ) m ( q + n C 2 / T ) / ( p + 4 - m ) ,
( L / K ) m - 1 = ( L / K ) m ( p + 5 - m ) ( q + n C 2 / T ) .
J ( λ ) = C 1 λ 5 exp ( - n C 2 / λ T ) ,             ρ ( λ ) = B m exp ( i m / λ ) . L = A C 1 B m 0 exp [ - 1 λ ( q + n C 2 / T - i m ) ] λ p + 5 d λ = A C 1 B m Γ ( p + 4 ) ( q + n C 2 / T - i m ) p + 4 .
J ( λ ) = m = 0 K m λ m .
L = A m = 0 K m Γ ( p - m - 1 ) q p - m - 1 .
J ( λ ) = m = 0 B m cos ( m / λ ) , L = A m = 0 B m R [ Γ ( p - 1 ) ( q - i m ) p - 1 ] .
J ( λ ) = m = 1 B m sin ( m / λ ) , L = A m = 1 B m J [ Γ ( p - 1 ) ( q - i m ) p - 1 ] .
J ( λ ) = C 1 λ 5 1 exp ( C 2 / λ T ) - 1 = C 1 λ 5 n = 1 exp [ - n C 2 / λ T ] .
L = A C 1 Γ ( p + 4 ) n = 1 ( q + n C 2 / T ) - ( p + 4 ) .
J ( λ ) = C 1 λ 5 1 exp ( C 2 / λ T ) - 1 ,             ρ ( λ ) = m = 1 K m λ m .
ρ ( λ ) J ( λ ) = C 1 λ 5 m = 1 n = 1 K m λ m exp ( - n C 2 / λ T ) ,
L = A C 1 m = 1 n = 1 K m Γ ( p + 4 - m ) ( q + n C 2 / T ) p + 4 - m .
ρ ( λ ) = m = 0 B m cos ( m / λ ) , L = A C 1 m = 0 n = 1 R [ B m Γ ( p + 4 ) ( q + n C 2 ) / ( T - i m ) p + 4 ] .
ρ ( λ ) = m = 1 B m sin ( m / λ ) , L = A C 1 m = 1 n = 1 J [ B m Γ ( p + 4 ) ( q + n C 2 ) / ( T - i m ) p + 4 ] .
x = x ¯ / ( x ¯ + z ¯ ) = const ,             z = z ¯ / ( x ¯ + z ¯ ) = const ,
L = 0 y ¯ ( λ ) J ( λ ) d λ = 0 y ¯ A ( λ ) J ( λ ) d λ - 0 y ¯ D ( λ ) J ( λ ) d λ .
log ( Y / K m ) = log A + log Γ ( p - m - 1 ) - ( p - m - 1 ) log q .
Y / K m = ( Y / K m ) A - ( Y / K m ) D .
L = 0 w ( λ ) J ( λ ) d λ .
X = 0.10666 641 munsell ; Y = 0.10685 351 young ;
Z = 0.10677             231 ostwald.
v t = 87 lumens / watt
Y = 2889.1             48502             youngs / m 2 .
D l = 60 π × 10 4 = 18849             55.592 lumens / m 2 .
D l / Y = 18849             55.592 2889.1             48502 = 652.426             lumens / young.
w ( λ ) J ( λ ) = A C 1 λ p + 5 exp [ - 1 λ ( q + n C 2 T ) ] .
d d λ [ w ( λ ) J ( λ ) ] = A C 1 exp [ - ( 1 / λ ) ( q + n C 2 / T ) ] λ p + 7 × [ - λ ( p + 5 ) + q + n C 2 / T ] .
- λ m ( p + 5 ) + q + n C 2 / T = 0 ,
λ m = ( q + n C 2 / T ) / ( p + 5 ) .
λ m = ( C 2 / 5 ) ( 1 / T ) ,
λ m T = 2864 ,
λ m = ( 100.93700 + 14320 / T ) / 187.19050.
[ w ( λ ) J ( λ ) ] max = A C 1 [ p + 5 q + n C 2 / T ] p + 5 exp [ - ( p + 5 ) ] .
( d 2 / d λ 2 ) [ w ( λ ) J ( λ ) ] = 0 ,
A C 1 exp [ - ( 1 / λ ) ( q + n C 2 / T ) ] λ p + q [ λ 2 ( p + 5 ) ( p + 6 ) - 2 λ ( p + 6 ) ( q + n C 2 / T ) + ( q + n C 2 / T ) 2 ] = 0.
λ = q + n C 2 / T p + 5 [ 1 ± ( 1 - ( p + 5 ) / ( p + 6 ) ) 1 2 ] .
w ( λ ) J ( λ ) = A C 1 exp [ - q / λ ] λ p + 5 × [ exp [ C 2 / ( λ T ) ] - 1 ] - 1 .
d d λ [ w ( λ ) J ( λ ) ] = - A C 1 x p + 6 exp ( - q x ) [ exp ( C 2 x / T ) - 1 ] 2 × { exp ( C 2 x / T ) · [ ( p + 5 ) - ( q + C 2 T ) x ] - ( p + 5 ) + q x } ,
exp ( C 2 x / T ) = ( p + 5 ) - q x ( p + 5 ) - ( q + C 2 / T ) x .
x m ( p + 5 ) / ( q + C 2 / T ) .
x m = a - Δ ,
a = ( p + 5 ) / ( q + C 2 / T ) .
K Δ exp ( - C 2 Δ / T ) = q Δ + C 2 a / T ,
K = ( q + C 2 / T ) exp ( C 2 a / T ) .
K Δ = q Δ + C 2 a / T ,
Δ = C 2 a / T ( K - q ) .
λ m = 1 x m = 1 / a [ 1 - C 2 T ( K - q ) ] .
λ m T = 2864 / [ 1 - exp ( - 5 ) ] = 2883.4.
1 + C 2 x T + C 2 x 2 2 T 2 + = [ ( p + 5 ) - q x ] [ ( p + 5 ) - q x ] - C 2 x / T . .
( C 2 x / T ) [ - 1 + ( p + 5 ) - q x m ] = 0 ,
λ m = q / ( p + 4 ) .
D l = A C 1 Γ ( p + 4 ) / ( q + n C 2 / T ) p + 4 ( young m - 2 ) ,
D r = σ T 4 ( watt m - 2 ) ,
v t = D l D r = A C 1 Γ ( p + 4 ) σ × 1 T 4 ( q + n C 2 / T ) p + 4 ( young watt - 1 ) .
v t T = A C 1 Γ ( p + 4 ) σ T 6 ( q + n C 2 / T ) p + 5 × [ - 4 T ( q + n C 2 / T ) + n C 2 ( p + 4 ) ] = 0.
T m = n C 2 p / 4 q ,
T m = 3580 p / q .
T m = 3580 ( 182.2 / 100.9 ) = 6450 ° K.
T m = 3580 ( 365.3 / 165.0 ) = 7930 ° K.
A = Planckian distribution at T = 2842 ° K ( C 2 = 14320 ) , B = Planckian distribution at T = 7000 ° K ( C 2 = 14320 ) .
x = X / ( X + Y + Z ) , y = Y / ( X + Y + Z ) .
L = A C 1 T / C 2 · Γ ( p + 3 ) / q p + 3 .
A Γ ( p + 3 ) / q p + 3 ,
x ¯ A ( λ ) = z ¯ ( λ ) / 4.570 ,             y ¯ C ( λ ) = 0.36678 13725 x ¯ C ( λ ) .