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  1. The reflection and the transmission factors for light are formally defined by the Illuminating Engineering Society (Rep. of Com. on Nomenclature and Standards, 1918). The terms are here used in accordance with these definitions, with the understanding, however, that they are determined under conditions of diffused light. Other symbols used in this article conform also with the I. E. S. nomenclature.
  2. Ann. d. Phys.,  316, p. 996; 1903. Good for reference to earlier work pertaining to Lambert’s law.See also in this connection Mascart Traite D’Optique, Vol.  3, p. 213.
    [Crossref]
  3. Loc. cit., p. 1006, Table I. (There appears to be a typographical error here in the record of angles.)
  4. “The Diffusion of Light,” Phil. Mag.,  35, p. 81; 1893.
    [Crossref]
  5. “Integrating The Sphere Photometric Construction Its and Use,” Tr. I. E. S.,  2, p. 453; 1916.
  6. “The Light Reflecting Values of White and Colored Paints,” J. F. I.,  181, p. 99; 1916.
  7. Tr. I. E. S., Vol.  7, p. 412; 1912.
  8. “Measurement of the Reflection Factor,” Elec. World, Vol.  69, p. 958; 1917.
  9. “Measurement of Diffuse Reflection Factors,” Jour. Am. Opt. Soc.,  4, p. 9; 1920.Also .
  10. Loc. cit., p. 16.
  11. G. E. Rev.,  23, p. 72; 1920.
  12. “A Simple Portable Reflectometer,” A. H. Taylor, Tr., I. E. S. Paper read at Fourteenth Annual Convention of I. E. S., 1920. Also .
  13. B. S. Bulletin, Vol.  7, p. 553; 1910.
  14. B. S. Bulletin, Vol.  6, p. 551; 1910.
  15. B. S. Bulletin, Vol.  6, p. 558; 1910.
  16. B. S. Bulletin, Vol.  6, No. 4, p. 562.
  17. Liebenthal, Praktische Photometric, p. 301.
  18. Electroteknische Zeit.,  21, p. 595; 1900,and Electroteknische Zeit. 26, p. 512; 1905.
  19. Palaz, “Traite de Photométrie Industrièlle,” Trans. by the Pattersons, p. 297.
  20. This reflectometer was shown before the Illuminating Engineering Society at Cleveland, Oct. 5, 1920.A general description of it will appear” in Trans. I. E. S., as discussion of the papers : “Measurement of Reflection Factor,” C. H. Sharp and W. F. Little;and “A Simple Portable Reflectometer of the Absolute Type,” A. H. Taylor
  21. Physikalische Zeitschrift, Vol.  1, pp. 299–303; 1900.
  22. It is to be regretted that this instrument is not more readily procurable.
  23. B. S. Sci. Papers, in press, “The Integrating Sphere,” Rosa and Taylor
  24. A. H. Taylor: “Measurement of Diffuse Reflection Factors and a New Absolute Reflectometer,” Jour. Am. Op. Soc., Vol.  4, No. 1, p. 9; 1920.
  25. F. A. Benford: “An Absolute Method for Determining Coefficients of Diffuse Reflection,” Gen. Elec. Rev., Vol.  23, p. 72; 1920.
  26. C. H. Sharp and W. F. Little: “Measurement of Reflection Factors,” Trans. I. E. S. Paper read at Fourteenth Annual Convention, I. E. S., 1920. See also paper by A. H. Taylor, presented at the same time; and discussion by Karrer.
  27. A. H. Taylor finds this angle to be about 50° for many surfaces. Prof. W. J. Drisko informs me that he has found the angle to be about 46° for many surfaces.
  28. Photographische Korrespondenz, May–June, 1910. Densograph, ein Registrierapparat zur Messung der Schwarrzung photographischer Platten.

1920 (4)

“Measurement of Diffuse Reflection Factors,” Jour. Am. Opt. Soc.,  4, p. 9; 1920.Also .

G. E. Rev.,  23, p. 72; 1920.

A. H. Taylor: “Measurement of Diffuse Reflection Factors and a New Absolute Reflectometer,” Jour. Am. Op. Soc., Vol.  4, No. 1, p. 9; 1920.

F. A. Benford: “An Absolute Method for Determining Coefficients of Diffuse Reflection,” Gen. Elec. Rev., Vol.  23, p. 72; 1920.

1917 (1)

“Measurement of the Reflection Factor,” Elec. World, Vol.  69, p. 958; 1917.

1916 (2)

“Integrating The Sphere Photometric Construction Its and Use,” Tr. I. E. S.,  2, p. 453; 1916.

“The Light Reflecting Values of White and Colored Paints,” J. F. I.,  181, p. 99; 1916.

1912 (1)

Tr. I. E. S., Vol.  7, p. 412; 1912.

1910 (4)

B. S. Bulletin, Vol.  7, p. 553; 1910.

B. S. Bulletin, Vol.  6, p. 551; 1910.

B. S. Bulletin, Vol.  6, p. 558; 1910.

Photographische Korrespondenz, May–June, 1910. Densograph, ein Registrierapparat zur Messung der Schwarrzung photographischer Platten.

1903 (1)

Ann. d. Phys.,  316, p. 996; 1903. Good for reference to earlier work pertaining to Lambert’s law.See also in this connection Mascart Traite D’Optique, Vol.  3, p. 213.
[Crossref]

1900 (2)

Electroteknische Zeit.,  21, p. 595; 1900,and Electroteknische Zeit. 26, p. 512; 1905.

Physikalische Zeitschrift, Vol.  1, pp. 299–303; 1900.

1893 (1)

“The Diffusion of Light,” Phil. Mag.,  35, p. 81; 1893.
[Crossref]

Benford, F. A.

F. A. Benford: “An Absolute Method for Determining Coefficients of Diffuse Reflection,” Gen. Elec. Rev., Vol.  23, p. 72; 1920.

Karrer,

C. H. Sharp and W. F. Little: “Measurement of Reflection Factors,” Trans. I. E. S. Paper read at Fourteenth Annual Convention, I. E. S., 1920. See also paper by A. H. Taylor, presented at the same time; and discussion by Karrer.

Liebenthal,

Liebenthal, Praktische Photometric, p. 301.

Little, W. F.

C. H. Sharp and W. F. Little: “Measurement of Reflection Factors,” Trans. I. E. S. Paper read at Fourteenth Annual Convention, I. E. S., 1920. See also paper by A. H. Taylor, presented at the same time; and discussion by Karrer.

Palaz,

Palaz, “Traite de Photométrie Industrièlle,” Trans. by the Pattersons, p. 297.

Rosa,

B. S. Sci. Papers, in press, “The Integrating Sphere,” Rosa and Taylor

Sharp, C. H.

C. H. Sharp and W. F. Little: “Measurement of Reflection Factors,” Trans. I. E. S. Paper read at Fourteenth Annual Convention, I. E. S., 1920. See also paper by A. H. Taylor, presented at the same time; and discussion by Karrer.

Taylor,

B. S. Sci. Papers, in press, “The Integrating Sphere,” Rosa and Taylor

Taylor, A. H.

A. H. Taylor: “Measurement of Diffuse Reflection Factors and a New Absolute Reflectometer,” Jour. Am. Op. Soc., Vol.  4, No. 1, p. 9; 1920.

C. H. Sharp and W. F. Little: “Measurement of Reflection Factors,” Trans. I. E. S. Paper read at Fourteenth Annual Convention, I. E. S., 1920. See also paper by A. H. Taylor, presented at the same time; and discussion by Karrer.

“A Simple Portable Reflectometer,” A. H. Taylor, Tr., I. E. S. Paper read at Fourteenth Annual Convention of I. E. S., 1920. Also .

Ann. d. Phys. (1)

Ann. d. Phys.,  316, p. 996; 1903. Good for reference to earlier work pertaining to Lambert’s law.See also in this connection Mascart Traite D’Optique, Vol.  3, p. 213.
[Crossref]

B. S. Bulletin (4)

B. S. Bulletin, Vol.  7, p. 553; 1910.

B. S. Bulletin, Vol.  6, p. 551; 1910.

B. S. Bulletin, Vol.  6, p. 558; 1910.

B. S. Bulletin, Vol.  6, No. 4, p. 562.

Elec. World (1)

“Measurement of the Reflection Factor,” Elec. World, Vol.  69, p. 958; 1917.

Electroteknische Zeit. (1)

Electroteknische Zeit.,  21, p. 595; 1900,and Electroteknische Zeit. 26, p. 512; 1905.

G. E. Rev. (1)

G. E. Rev.,  23, p. 72; 1920.

Gen. Elec. Rev. (1)

F. A. Benford: “An Absolute Method for Determining Coefficients of Diffuse Reflection,” Gen. Elec. Rev., Vol.  23, p. 72; 1920.

J. F. I. (1)

“The Light Reflecting Values of White and Colored Paints,” J. F. I.,  181, p. 99; 1916.

Jour. Am. Op. Soc. (1)

A. H. Taylor: “Measurement of Diffuse Reflection Factors and a New Absolute Reflectometer,” Jour. Am. Op. Soc., Vol.  4, No. 1, p. 9; 1920.

Jour. Am. Opt. Soc. (1)

“Measurement of Diffuse Reflection Factors,” Jour. Am. Opt. Soc.,  4, p. 9; 1920.Also .

Loc. cit. (2)

Loc. cit., p. 16.

Loc. cit., p. 1006, Table I. (There appears to be a typographical error here in the record of angles.)

Phil. Mag. (1)

“The Diffusion of Light,” Phil. Mag.,  35, p. 81; 1893.
[Crossref]

Photographische Korrespondenz (1)

Photographische Korrespondenz, May–June, 1910. Densograph, ein Registrierapparat zur Messung der Schwarrzung photographischer Platten.

Physikalische Zeitschrift (1)

Physikalische Zeitschrift, Vol.  1, pp. 299–303; 1900.

Tr. I. E. S. (2)

“Integrating The Sphere Photometric Construction Its and Use,” Tr. I. E. S.,  2, p. 453; 1916.

Tr. I. E. S., Vol.  7, p. 412; 1912.

Other (9)

“A Simple Portable Reflectometer,” A. H. Taylor, Tr., I. E. S. Paper read at Fourteenth Annual Convention of I. E. S., 1920. Also .

Palaz, “Traite de Photométrie Industrièlle,” Trans. by the Pattersons, p. 297.

This reflectometer was shown before the Illuminating Engineering Society at Cleveland, Oct. 5, 1920.A general description of it will appear” in Trans. I. E. S., as discussion of the papers : “Measurement of Reflection Factor,” C. H. Sharp and W. F. Little;and “A Simple Portable Reflectometer of the Absolute Type,” A. H. Taylor

Liebenthal, Praktische Photometric, p. 301.

It is to be regretted that this instrument is not more readily procurable.

B. S. Sci. Papers, in press, “The Integrating Sphere,” Rosa and Taylor

The reflection and the transmission factors for light are formally defined by the Illuminating Engineering Society (Rep. of Com. on Nomenclature and Standards, 1918). The terms are here used in accordance with these definitions, with the understanding, however, that they are determined under conditions of diffused light. Other symbols used in this article conform also with the I. E. S. nomenclature.

C. H. Sharp and W. F. Little: “Measurement of Reflection Factors,” Trans. I. E. S. Paper read at Fourteenth Annual Convention, I. E. S., 1920. See also paper by A. H. Taylor, presented at the same time; and discussion by Karrer.

A. H. Taylor finds this angle to be about 50° for many surfaces. Prof. W. J. Drisko informs me that he has found the angle to be about 46° for many surfaces.

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Figures (7)

F. 1
F. 1

Infinite planes.

F. 2
F. 2

A disk S surrounded by annular areas ss of lesser brightness.

F. 3
F. 3

The sphere reflectometer using the Koenig-Martens polarization photometer.

F. 4
F. 4

A simple and inexpensive reflectometer for commercial use.

F. 5
F. 5

An absolute transmissometer using two spheres.

F. 6
F. 6

The transmissometer in horizontal section; showing the position of the light source, test sample, photometer and screens.

F. 7
F. 7

An absolute transmissometer using one sphere only and the Koenig-Martens polarization photometer.

Equations (28)

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E 2 E 1 + E 2 = ρ
E 1 E 1 + E 2 = α = 1 ρ
ρ 2 [ q ( p + q 1 ) + b b 0 p ( 1 q ) ] + ρ ( 1 q ) [ q + ( p + q 1 ) ( 1 b b 0 ) ] + ( 1 q ) 2 ( 1 b b 0 ) = 0
ρ = b 1 b 2 b 1 p 1 b 2 p 2
ρ x = 1 b 0 b x q 1 q · b 0 b x + ρ p ρ p + ( 1 q ) ( 1 ρ )
ρ b x b 1 ρ 2 p ( 1 b x b ) 1 q + ρ ( p + q 1 )
b s = pb · ρ 1 ρ
E T = π b + π ρ 1 ρ 2 b + π ρ 1 2 ρ 2 2 b + · · + etc .
b T = ρ 1 b ( 1 + ρ 1 ρ 2 + ρ 1 2 ρ 2 2 + + ρ 1 n 1 ρ 2 n 1 + + ) = ρ 1 b / ( 1 ρ 1 ρ 2 ) .
b S = b ( 1 + ρ 1 ρ 2 + ρ 1 2 ρ 2 2 + + ρ 1 n + 1 ρ 2 n + 1 + · · + ) = b / ( 1 ρ 1 ρ 2 ) . b T / b S = ρ 1 .
E d = π b 0 a 2 r 2 x dx ( r 2 + x 2 ) 2 = π b a 2 r 2 + a 2
E 1 = π b 1 a 3 a 2 r 2 x dx ( r 2 + x 2 ) 2 = 8 π b 1 a 2 r 2 ( r 2 + 9 a 2 ) ( r 2 + a 2 ) .
E t = π ba 2 ( r 2 + a 2 ) ( 1 + 8 ρ m r 2 r 2 + 9 a 2 ) .
E t = 2 π br 2 0 3 a xdx ( r 2 + x 2 ) 2 = 9 π ba 2 ( r 2 + 9 a 2 ) .
E n = π b ρ m n a ( 2 n 1 ) a ( 2 n + 1 ) 2 r 2 x dx ( r 2 + x 2 ) 2 = 8 π ba 2 r 2 n ρ m n [ r 2 + ( 2 n 1 ) 2 a 2 ] [ r 2 + ( 2 n + 1 ) 2 a 2 ]
E a = n = 1 n = π b ρ m n a ( 2 n 1 ) a ( 2 n + 1 ) 2 r 2 x dx ( r 2 + x 2 ) 2 = n = 1 n = 8 π ba 2 r 2 n ρ m n [ r 2 + ( 2 n 1 ) 2 a 2 ] [ r 2 + ( 2 n + 1 ) 2 a 2 ] .
E t = E d + E a = π ba 2 { 1 r 2 + a 2 + 8 r 2 n = 1 n = n ρ m n [ r 2 + ( 2 n 1 ) 2 a 2 ] [ r 2 + ( 2 n + 1 ) 2 a 2 ] } .
E t = π ba 2 [ 1 a 2 + r 2 + 8 r 2 { ρ m ( r 2 + 9 a 2 ) ( r 2 + a 2 ) + 2 ρ m 2 ( r 2 + 25 a 2 ) ( r 2 + 9 a 2 ) + + } + 8 r 2 { n ρ m n [ r 2 + ( 2 n 1 ) 2 a 2 ] [ r 2 + ( 2 n + 1 ) 2 a 2 ] + ( n + 1 ) ρ m n + 1 [ r 2 + ( 2 n + 3 ) 2 a 2 ] [ r 2 + ( 2 n + 1 ) 2 a 2 ] + + } ] .
ρ m · n + 1 n { 1 ( 8 + 16 n ) a 2 r 2 + ( 2 n + 3 ) 2 a 2 } ,
e = 8 r 2 n ρ m n ( a 2 + r 2 ) [ r 2 + ( 2 n + 1 ) 2 a 2 ] [ r 2 + ( 2 n 1 ) 2 a 2 ] .
α F = π bA . F = π bA α = π bA ( 1 ρ )
E = bA 4 r 2 · 1 1 ρ .
ρ bA 4 π r 2 · 1 1 ρ = b S .
A 4 π r 2 = p
b S = pb ρ 1 ρ .
b x = ρ x bp 1 ρ = ρ x b S ρ . b x / b S = ρ x / ρ .
b x b S = ρ x .
b x = b ( ρ + τ ) . b x / b = ρ + τ .