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  1. W. Harrison and E. A. Anderson, “Illumination efficiencies as determined in an experimental room,” Trans. I.E.S. 11, 67 (1916).
  2. W. Harrison and E. A. Anderson, “Coefficients of utilization,” Trans. I.E.S. 15, 97 (1920).
  3. J. Dourgnon, “Nouvelle méthode de prédétermination des coefficients d’utilisation dans les projets d’éclairage d’espaces clos,” Gen. Elec. Rev. 23, 271 (1928). J. Dourgnon, “Définition et calcul des grandeurs caractéristiques de l’éclairage d’un espace clos,” Gen. Elec. Rev. 33, 579 (1933).
  4. K. Hisano, “Light flux distribution in a rectangular parallelepiped and its simplifying scale,” Res. Elec. Lab., Tokyo, No. 394 (1936). [In Japanese.]
  5. J. Wetzel, “Nouvelle méthode de calcul des coefficients d’utilisation,” C.I.E. Proc. p. 517 (1931).
  6. W. Margoulis, “Etude nomographique pour la détermination des coefficients d’utilisation dans les projets d’éclairage,” Gen. Elec. Rev. 24, 439 (1928).
  7. A. Vallat, “Les méthodes d’évaluation des facteurs d’utilisation,” Comptes rendus Congres Int. des Appl. de l’Eclairage (Paris, 1937), p. 137.
  8. H. L. Logan, “Specification points of brightness,” Trans. I.E.S. 34, 881 (1939).
  9. Parry Moon, “Interreflections in finite cylinders,” J. Opt. Soc. Am. 31, 223 (1941).
    [CrossRef]
  10. Parry Moon, “Interreflections in lightwells,” J. Opt. Soc. Am. 31, 301 (1941).
    [CrossRef]
  11. Reference 2, p. 123.
  12. Reference 1, p. 74.
  13. Parry Moon, Scientific Basis of Illuminating Engineering (McGraw-Hill, New York, 1936).

1941 (2)

1939 (1)

H. L. Logan, “Specification points of brightness,” Trans. I.E.S. 34, 881 (1939).

1931 (1)

J. Wetzel, “Nouvelle méthode de calcul des coefficients d’utilisation,” C.I.E. Proc. p. 517 (1931).

1928 (2)

W. Margoulis, “Etude nomographique pour la détermination des coefficients d’utilisation dans les projets d’éclairage,” Gen. Elec. Rev. 24, 439 (1928).

J. Dourgnon, “Nouvelle méthode de prédétermination des coefficients d’utilisation dans les projets d’éclairage d’espaces clos,” Gen. Elec. Rev. 23, 271 (1928). J. Dourgnon, “Définition et calcul des grandeurs caractéristiques de l’éclairage d’un espace clos,” Gen. Elec. Rev. 33, 579 (1933).

1920 (1)

W. Harrison and E. A. Anderson, “Coefficients of utilization,” Trans. I.E.S. 15, 97 (1920).

1916 (1)

W. Harrison and E. A. Anderson, “Illumination efficiencies as determined in an experimental room,” Trans. I.E.S. 11, 67 (1916).

Anderson, E. A.

W. Harrison and E. A. Anderson, “Coefficients of utilization,” Trans. I.E.S. 15, 97 (1920).

W. Harrison and E. A. Anderson, “Illumination efficiencies as determined in an experimental room,” Trans. I.E.S. 11, 67 (1916).

Dourgnon, J.

J. Dourgnon, “Nouvelle méthode de prédétermination des coefficients d’utilisation dans les projets d’éclairage d’espaces clos,” Gen. Elec. Rev. 23, 271 (1928). J. Dourgnon, “Définition et calcul des grandeurs caractéristiques de l’éclairage d’un espace clos,” Gen. Elec. Rev. 33, 579 (1933).

Harrison, W.

W. Harrison and E. A. Anderson, “Coefficients of utilization,” Trans. I.E.S. 15, 97 (1920).

W. Harrison and E. A. Anderson, “Illumination efficiencies as determined in an experimental room,” Trans. I.E.S. 11, 67 (1916).

Hisano, K.

K. Hisano, “Light flux distribution in a rectangular parallelepiped and its simplifying scale,” Res. Elec. Lab., Tokyo, No. 394 (1936). [In Japanese.]

Logan, H. L.

H. L. Logan, “Specification points of brightness,” Trans. I.E.S. 34, 881 (1939).

Margoulis, W.

W. Margoulis, “Etude nomographique pour la détermination des coefficients d’utilisation dans les projets d’éclairage,” Gen. Elec. Rev. 24, 439 (1928).

Moon, Parry

Vallat, A.

A. Vallat, “Les méthodes d’évaluation des facteurs d’utilisation,” Comptes rendus Congres Int. des Appl. de l’Eclairage (Paris, 1937), p. 137.

Wetzel, J.

J. Wetzel, “Nouvelle méthode de calcul des coefficients d’utilisation,” C.I.E. Proc. p. 517 (1931).

C.I.E. Proc. (1)

J. Wetzel, “Nouvelle méthode de calcul des coefficients d’utilisation,” C.I.E. Proc. p. 517 (1931).

Gen. Elec. Rev. (2)

W. Margoulis, “Etude nomographique pour la détermination des coefficients d’utilisation dans les projets d’éclairage,” Gen. Elec. Rev. 24, 439 (1928).

J. Dourgnon, “Nouvelle méthode de prédétermination des coefficients d’utilisation dans les projets d’éclairage d’espaces clos,” Gen. Elec. Rev. 23, 271 (1928). J. Dourgnon, “Définition et calcul des grandeurs caractéristiques de l’éclairage d’un espace clos,” Gen. Elec. Rev. 33, 579 (1933).

J. Opt. Soc. Am. (2)

Trans. I.E.S. (3)

W. Harrison and E. A. Anderson, “Illumination efficiencies as determined in an experimental room,” Trans. I.E.S. 11, 67 (1916).

W. Harrison and E. A. Anderson, “Coefficients of utilization,” Trans. I.E.S. 15, 97 (1920).

H. L. Logan, “Specification points of brightness,” Trans. I.E.S. 34, 881 (1939).

Other (5)

Reference 2, p. 123.

Reference 1, p. 74.

Parry Moon, Scientific Basis of Illuminating Engineering (McGraw-Hill, New York, 1936).

K. Hisano, “Light flux distribution in a rectangular parallelepiped and its simplifying scale,” Res. Elec. Lab., Tokyo, No. 394 (1936). [In Japanese.]

A. Vallat, “Les méthodes d’évaluation des facteurs d’utilisation,” Comptes rendus Congres Int. des Appl. de l’Eclairage (Paris, 1937), p. 137.

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Figures (12)

Fig. 1
Fig. 1

Rectangular room.

Fig. 2
Fig. 2

Average illumination on a horizontal plane. Cubical room, h=0.75, ρ3=0. Curves, calculated by use of Eq. (10). Points, experimental values of Harrison and Anderson (see reference 2).

Fig. 3
Fig. 3

Average ceiling luminosity. Cubical room, ρ3=0.

Fig. 4
Fig. 4

Effect of table height. Cubical room, ρ2=0.80; ρ3=0.

Fig. 5
Fig. 5

Effect of table height. Large room, l=0.20, ρ1=0, ρ2=0.80.

Fig. 6
Fig. 6

Effect of the floor on the average illumination. Cubical room, ρ2=0.80, h=0.75.

Fig. 7
Fig. 7

Effect of the floor on the ceiling luminosity. Cubical room, ρ2=0.80.

Fig. 8
Fig. 8

Luminosity distribution on the walls of a cubical room. ρ1=ρ2=0.80.

Fig. 9
Fig. 9

Effect of floor. Large room, l=0.20, h=0.15, ρ1=0, ρ2=0.80.

Fig. 10
Fig. 10

Effect of room shape on the average illumination. ρ2=0.80, h/l=0.75.

Fig. 11
Fig. 11

Effect of room shape on the ceiling luminosity, ρ2=0.80.

Fig. 12
Fig. 12

Effect of room shape on the floor luminosity, ρ2=0.80.

Equations (20)

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L 1 ( s ) = B cosh k s + C sinh k s ,
B = ρ 1 L 02 n ( 1 - ρ 2 ) n + ( 1 - ρ 1 ) 1 2 ( 1 + ρ 2 ) m ,
C = - ρ 1 L 02 m ( 1 - ρ 2 ) n + ( 1 - ρ 1 ) 1 2 ( 1 - ρ 2 ) m , m = ( 1 - ρ 3 ) cosh k l + ( 1 - ρ 1 ) 1 2 ( 1 + ρ 3 ) sinh k l , n = ( 1 - ρ 3 ) sinh k l + ( 1 - ρ 1 ) 1 2 ( 1 + ρ 3 ) cosh k l .
L 2 ( l ) = 1 1 - ρ 2 ρ 3 e - 2 α l { L 02 + ρ 2 e - a l [ B ρ 1 [ v 3 - m ] + C ρ 1 [ ( 1 - ρ 1 ) 1 2 u 3 - n ] ] } .
L 3 ( l ) = ρ 3 e - a l 1 - ρ 2 ρ 3 e - 2 a l { L 02 + B ρ 1 [ v 2 cosh k l - ( 1 - ρ 1 ) 1 2 u 2 sinh k l - ( 1 - ρ 2 ) ] + C ρ 1 [ u 2 sinh k l - ( 1 - ρ 1 ) 1 2 u 2 cosh k l + ( 1 - ρ 1 ) 1 2 ( 1 + ρ 2 ) ] } ,
u 2 = e a l + ρ 2 e - a l ,             v 2 = e a l - ρ 2 e - a l ,             u 3 = e a l + ρ 3 e - a l ,             v 3 = e a l - ρ 3 e - a l .
E Av ( h ) = L 2 e - a h + B ρ 1 { cosh k h - ( 1 - ρ 1 ) 1 2 sinh k h - e - a h } + C ρ 1 { sinh k h - ( 1 - ρ 1 ) 1 2 cosh k h + ( 1 - ρ 1 ) 1 2 e - a h } .
E Av = 4 L 2 π [ ( h 2 + 1 ) 1 2 tan - 1 ( h 2 + 1 ) - 1 2 - h tan - 1 ( 1 / h ) + h 2 2 ln h 2 + 1 ( h 2 + 2 ) 1 2 ]
L 1 ( s ) = ρ 1 L 02 T [ R cosh k s - S sinh k s ] ,
R = ( 1 - ρ 1 ) 1 2 cosh k l + sinh k l , S = cosh k l + ( 1 - ρ 1 ) 1 2 sinh k l , T = 2 ( 1 - ρ 1 ) 1 2 cosh k l + [ ( 1 - ρ 2 ) + ( 1 - ρ 1 ) ( 1 + ρ 2 ) ] sinh k l , L 2 = L 02 ( 1 + ρ 1 ρ 2 sinh k l T ) , L 3 = 0 ,
E Av ( h ) = L 2 e - a h + R T { cosh k h - ( 1 - ρ 1 ) 1 2 sinh k h - e - a h } - S T { sin k h - ( 1 - ρ 1 ) 1 2 cosh k h + ( 1 - ρ 1 ) 1 2 e - a h } .
L 1 ( s ) = 0 , L 2 = L 02 1 - ρ 2 ρ 3 e - 2 a l ,
L 3 = ρ 3 L 02 e - a l 1 - ρ 2 ρ 3 e - 2 a l ,
E Av ( h ) = L 2 e - a h .
1.04 / 0.27 ( 0.80 ) = 4.8 ,
1.35 / 0.64 ( 0.80 ) = 2.6.
E Av ρ 2 / L 02 .
k r = W 1 / ( 0.9 W 2 + 0.1 W 3 )             ( W 2 W 3 ) .
k r = W 1 ( W 2 + W 3 ) / 2 W 2 W 3 .
k r = W 1 / W 2 = W 1 / W 3