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  1. Skinner, Phys. Rev.,  9, p. 148; 1917.
    [CrossRef]
  2. Drude, Ann. d. Phys.,  32, p. 584; 1887.
    [CrossRef]
  3. Drude. Ann. d. Phys.,  34, p. 489; 1888.
    [CrossRef]
  4. Müller, Neues Yahrb. für Mineral, u.s.w. 17, p. 187; 1903.
  5. Weld, J. O. S. A. and R. S. I. 6, p. 67; 1922.
    [CrossRef]
  6. Loc. cit.
  7. In the Babinet Compensator method as employed by Skinner, no serious difficulties in reducing the results arose, because in that method one adjusts conditions until a phase difference of 90° is introduced. The formulas, for purposes of calculation, are thus vastly simplified. In Weld’s apparatus, on the other hand, one obtains a photographic record, and from this calculates the phase differences. It would involve an inordinate labor to repeat observations until a value of 90° for the phase difference were found.
  8. Drude, Ann. d. Phys. 34, p. 489; 1888.
    [CrossRef]
  9. Müller, Loc. cit.
  10. Loc. cit. 1887.
  11. Drude, loc. cit. pp. 618–620; 1887.
  12. Weld, loc. cit. p. 90.
  13. Loc. cit. 1888.
  14. Loc. cit.
  15. Loc. cit.
  16. Weld gives Δ, as 20° 41′, etc., but if the light is viewed as it comes toward an observer, his expression ∇, or π+20° 41′ must be employed. Drude’s equations are developed on this basis.
  17. Loc. cit. 1887. There is a change in the use of the letters α, β, and γ in Drude’s two papers. Careful reading will obviate any confusion.
  18. Wood, Phil. Mag. 3, p. 612; 1902.
  19. Sieg, Proc. Ia. Acad. Sci. 23, p. 179; 1916.
  20. Ann. der Phys. 43, p. 1227; 1914.
  21. Pfund, Phys. Zeit. 10, p. 340; 1909.
  22. Grippenberg, Phys. Zeit. 22, p. 281; 1921.

1922 (1)

Weld, J. O. S. A. and R. S. I. 6, p. 67; 1922.
[CrossRef]

1921 (1)

Grippenberg, Phys. Zeit. 22, p. 281; 1921.

1917 (1)

Skinner, Phys. Rev.,  9, p. 148; 1917.
[CrossRef]

1916 (1)

Sieg, Proc. Ia. Acad. Sci. 23, p. 179; 1916.

1914 (1)

Ann. der Phys. 43, p. 1227; 1914.

1909 (1)

Pfund, Phys. Zeit. 10, p. 340; 1909.

1903 (1)

Müller, Neues Yahrb. für Mineral, u.s.w. 17, p. 187; 1903.

1902 (1)

Wood, Phil. Mag. 3, p. 612; 1902.

1888 (2)

Drude. Ann. d. Phys.,  34, p. 489; 1888.
[CrossRef]

Drude, Ann. d. Phys. 34, p. 489; 1888.
[CrossRef]

1887 (1)

Drude, Ann. d. Phys.,  32, p. 584; 1887.
[CrossRef]

Drude,

Drude, Ann. d. Phys. 34, p. 489; 1888.
[CrossRef]

Drude. Ann. d. Phys.,  34, p. 489; 1888.
[CrossRef]

Drude, Ann. d. Phys.,  32, p. 584; 1887.
[CrossRef]

Drude, loc. cit. pp. 618–620; 1887.

Grippenberg,

Grippenberg, Phys. Zeit. 22, p. 281; 1921.

Müller,

Müller, Neues Yahrb. für Mineral, u.s.w. 17, p. 187; 1903.

Müller, Loc. cit.

Pfund,

Pfund, Phys. Zeit. 10, p. 340; 1909.

Sieg,

Sieg, Proc. Ia. Acad. Sci. 23, p. 179; 1916.

Skinner,

Skinner, Phys. Rev.,  9, p. 148; 1917.
[CrossRef]

Weld,

Weld, J. O. S. A. and R. S. I. 6, p. 67; 1922.
[CrossRef]

Weld, loc. cit. p. 90.

Wood,

Wood, Phil. Mag. 3, p. 612; 1902.

Ann. d. Phys. (3)

Drude, Ann. d. Phys. 34, p. 489; 1888.
[CrossRef]

Drude, Ann. d. Phys.,  32, p. 584; 1887.
[CrossRef]

Drude. Ann. d. Phys.,  34, p. 489; 1888.
[CrossRef]

Ann. der Phys. (1)

Ann. der Phys. 43, p. 1227; 1914.

J. O. S. A. and R. S. I. (1)

Weld, J. O. S. A. and R. S. I. 6, p. 67; 1922.
[CrossRef]

Neues Yahrb. für Mineral, u.s.w. (1)

Müller, Neues Yahrb. für Mineral, u.s.w. 17, p. 187; 1903.

Phil. Mag. (1)

Wood, Phil. Mag. 3, p. 612; 1902.

Phys. Rev. (1)

Skinner, Phys. Rev.,  9, p. 148; 1917.
[CrossRef]

Phys. Zeit. (2)

Pfund, Phys. Zeit. 10, p. 340; 1909.

Grippenberg, Phys. Zeit. 22, p. 281; 1921.

Proc. Ia. Acad. Sci. (1)

Sieg, Proc. Ia. Acad. Sci. 23, p. 179; 1916.

Other (11)

Loc. cit.

In the Babinet Compensator method as employed by Skinner, no serious difficulties in reducing the results arose, because in that method one adjusts conditions until a phase difference of 90° is introduced. The formulas, for purposes of calculation, are thus vastly simplified. In Weld’s apparatus, on the other hand, one obtains a photographic record, and from this calculates the phase differences. It would involve an inordinate labor to repeat observations until a value of 90° for the phase difference were found.

Müller, Loc. cit.

Loc. cit. 1887.

Drude, loc. cit. pp. 618–620; 1887.

Weld, loc. cit. p. 90.

Loc. cit. 1888.

Loc. cit.

Loc. cit.

Weld gives Δ, as 20° 41′, etc., but if the light is viewed as it comes toward an observer, his expression ∇, or π+20° 41′ must be employed. Drude’s equations are developed on this basis.

Loc. cit. 1887. There is a change in the use of the letters α, β, and γ in Drude’s two papers. Careful reading will obviate any confusion.

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Figures (6)

Fig. 1
Fig. 1

Orientation of crystal with respect to plane of incidence.

Fig. 2
Fig. 2

Variation of the absorption coefficient with the wave-length, in the two principal positions.

Fig. 3
Fig. 3

Variation of the index of refraction with the wave-length in the two principal positions.

Fig. 4
Fig. 4

Variation of the reflecting power with the wave-length in the two principal positions.

Fig. 5
Fig. 5

Arrangement of spectrophotometer for determining the reflecting powers of small surfaces.

Fig. 6
Fig. 6

Experimental determination of the principal reflecting powers of an isolated selenium crystal, compared with previous results on cast selenium plates.

Tables (1)

Tables Icon

Table 1 Φ=60°.

Equations (22)

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r = R s R p e i Δ = tan Ψ · e i Δ
r 1 = cos Φ - α 1 - α sin 2 Φ cos Φ + α 1 - α sin 2 Φ · γ cos Φ + 1 - γ sin 2 Φ γ cos Φ - 1 - γ sin 2 Φ r 2 = α cos Φ + 1 - α sin 2 Φ α cos Φ - 1 - α sin 2 Φ · cos Φ - γ 1 - α sin 2 Φ cos Φ + γ 1 - α sin 2 Φ }
R 1 = 1 + r 1 1 - r 1 = cos 2 Ψ 1 1 - sin 2 Ψ , cos Δ 1 + i sin 2 Ψ 1 sin Δ 1 1 - sin 2 Ψ , cos Δ 1 R 2 = 1 + r 2 1 - r 2 = cos 2 Ψ 2 1 - sin 2 Ψ 2 cos Δ 2 + i sin 2 Ψ 2 sin Δ 2 1 - sin 2 Ψ 2 cos Δ 2 }
sin 2 Φ = A 2 , cos 2 Φ = B 2 , α = x , γ = y
R 1 = B 2 y - x 1 - A 2 x 2 1 - A 2 y 2 B x y 1 - x 2 A 2 - B 1 - A 2 y 2 R 2 = B 2 x - y ( 1 - A 2 x 2 ) ( x y - 1 ) B 1 - A 2 x 2 }
1 - A 2 x 2 = 1 - A 2 x 2 2 - .
R 1 = - B y + x B - A 2 2 B x 3 - A 2 B 2 y 3 + x 2 y B - B x y 2 + . R 2 = - B x + y B - B A 2 2 x 3 + x y 2 B - A 2 + 2 B 2 2 B 2 · x 2 y + . }
Δ 1 = π + 20 ° 4 1 Ψ 1 = 24 ° 2 6 Δ 2 = π + 4 ° 2 6 Ψ 2 = 32 ° 2 7
R 1 = 0.386 - 0.156 i R 2 = 0.223 - 0.037 i }
.386 - .156 i = 2 x - y / 2 - 3 / 4 x 3 - 3 / 16 y 3 - x y 2 / 2 + 2 x 2 y .223 - .037 i = - x / 2 + 2 y - 3 / 16 x 3 + 2 x y 2 - 5 / 4 x 2 y }
x = .236 - .088 i y = .170 - .041 i }
Δ R 1 = - .0038 + .004 i Δ R 2 = - .0009 - .0026 i
- .0038 + .004 i = ( 2 - 9 / 4 x 2 - y 2 / 2 + 4 x y ) Δ x + ( 2 x 2 - x y - 9 / 16 y 2 - 1 / 2 ) Δ y - .0009 - .0026 i = ( 2 y 2 - 5 / 2 x y - 9 / 16 x 2 - 1 / 2 ) Δ x + ( 2 + 4 x y - 5 / 4 x 2 ) Δ y
- .0038 + .004 i = ( 2.0244 + .0015 i ) Δ x + ( - .4558 - .0505 i ) Δ y - .0009 - .0026 i = ( - .5638 + .0572 i ) Δ x + ( 2.0860 - .0469 i ) Δ y
Δ x = - .00207 + .00179 i , Δ y = - .00092 - .00073 i
x = x + Δ x = .234 - .086 i y = y + Δ y = .169 - .042 i }
R 1 = .387 - .155 i R 2 = .222 - .039 i }
α = a 11 + i a 12 β = a 21 + i a 22 γ = a 31 + i a 32
tan X = a 32 a 31 ,             tan = a 12 a 11 ,
k 1 = tan X / 2 ,             k 2 = tan / 2 ,
n 1 2 = 2 ( sin X / 2 ) ( cos 3 X / 2 ) a 32 , n 2 2 = 2 ( sin / 2 ) ( cos 3 / 2 ) a 12 ,
P = n 2 ( 1 + k 2 ) + 1 - 2 n n 2 ( 1 + k 2 ) + 1 + 2 n ,