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  1. cf. Scheibner and Koenig. Sachsischen Ges. Wiss., p. 541; 1878.
  2. Harting, Zts. Instk.1908.
  3. Keeler: Publications of the Astron. Soc of the PacificNov., 1890.
  4. v. Merz, Zts. Instk 18, p. 288; 1898 (Referat) Steinheil, Zts. Instk. 19, p. 177; 1899.
  5. Czapski, Zts. Instk.,  6, p. 342; 1888.
  6. Taylor, Monthly Notices Royal Astr. Soc.,  54, p. 67; 1894.
  7. Harting, Zts. Instk.,  31, p. 72; 1911.
  8. Wilsing, Zts. Instk.,  26, p. 41, 1906.
  9. Zs. Instk.,  19, p. 57, 1899. (Referat.)Zs. Instk.,  37, p. 166; 1917.
  10. Harting, Zs. Instk.,  28, p. 273; 1908.
  11. Wilsing: Zs. Instk.,  26, p. 41; 1906.
  12. Wolf: Zts. Instk.,  19, p. 1; 1899.
  13. H. Dennis Taylor: Monthly Notices, Royal Astr. Soc., p. 309, March, 1894, System of Applied Optics.
  14. Loc. cit.
  15. Zts. Instk.,  17, p. 50, p. 77; 1897.
  16. , 1921, on “Spectral Distribution of Energy required to evoke the Gray Sensation.”
  17. Loc. cit. p. 245.
  18. Cf.J. W. Gifford, Nature 114, p. 645, 1924.
    [CrossRef]

1924 (1)

Cf.J. W. Gifford, Nature 114, p. 645, 1924.
[CrossRef]

1911 (1)

Harting, Zts. Instk.,  31, p. 72; 1911.

1908 (2)

Harting, Zts. Instk.1908.

Harting, Zs. Instk.,  28, p. 273; 1908.

1906 (2)

Wilsing: Zs. Instk.,  26, p. 41; 1906.

Wilsing, Zts. Instk.,  26, p. 41, 1906.

1899 (2)

Zs. Instk.,  19, p. 57, 1899. (Referat.)Zs. Instk.,  37, p. 166; 1917.

Wolf: Zts. Instk.,  19, p. 1; 1899.

1898 (1)

v. Merz, Zts. Instk 18, p. 288; 1898 (Referat) Steinheil, Zts. Instk. 19, p. 177; 1899.

1897 (1)

Zts. Instk.,  17, p. 50, p. 77; 1897.

1894 (2)

H. Dennis Taylor: Monthly Notices, Royal Astr. Soc., p. 309, March, 1894, System of Applied Optics.

Taylor, Monthly Notices Royal Astr. Soc.,  54, p. 67; 1894.

1890 (1)

Keeler: Publications of the Astron. Soc of the PacificNov., 1890.

1888 (1)

Czapski, Zts. Instk.,  6, p. 342; 1888.

1878 (1)

cf. Scheibner and Koenig. Sachsischen Ges. Wiss., p. 541; 1878.

Czapski,

Czapski, Zts. Instk.,  6, p. 342; 1888.

Gifford, J. W.

Cf.J. W. Gifford, Nature 114, p. 645, 1924.
[CrossRef]

Harting,

Harting, Zts. Instk.,  31, p. 72; 1911.

Harting, Zts. Instk.1908.

Harting, Zs. Instk.,  28, p. 273; 1908.

Keeler,

Keeler: Publications of the Astron. Soc of the PacificNov., 1890.

Koenig,

cf. Scheibner and Koenig. Sachsischen Ges. Wiss., p. 541; 1878.

Scheibner,

cf. Scheibner and Koenig. Sachsischen Ges. Wiss., p. 541; 1878.

Taylor,

Taylor, Monthly Notices Royal Astr. Soc.,  54, p. 67; 1894.

Taylor, H. Dennis

H. Dennis Taylor: Monthly Notices, Royal Astr. Soc., p. 309, March, 1894, System of Applied Optics.

v. Merz,

v. Merz, Zts. Instk 18, p. 288; 1898 (Referat) Steinheil, Zts. Instk. 19, p. 177; 1899.

Wilsing,

Wilsing: Zs. Instk.,  26, p. 41; 1906.

Wilsing, Zts. Instk.,  26, p. 41, 1906.

Wolf,

Wolf: Zts. Instk.,  19, p. 1; 1899.

Loc. cit. (1)

Loc. cit.

Monthly Notices Royal Astr. Soc. (1)

Taylor, Monthly Notices Royal Astr. Soc.,  54, p. 67; 1894.

Monthly Notices, Royal Astr. Soc. (1)

H. Dennis Taylor: Monthly Notices, Royal Astr. Soc., p. 309, March, 1894, System of Applied Optics.

Nature (1)

Cf.J. W. Gifford, Nature 114, p. 645, 1924.
[CrossRef]

Publications of the Astron. Soc of the Pacific (1)

Keeler: Publications of the Astron. Soc of the PacificNov., 1890.

Sachsischen Ges. Wiss. (1)

cf. Scheibner and Koenig. Sachsischen Ges. Wiss., p. 541; 1878.

Zs. Instk. (3)

Zs. Instk.,  19, p. 57, 1899. (Referat.)Zs. Instk.,  37, p. 166; 1917.

Harting, Zs. Instk.,  28, p. 273; 1908.

Wilsing: Zs. Instk.,  26, p. 41; 1906.

Zts. Instk (1)

v. Merz, Zts. Instk 18, p. 288; 1898 (Referat) Steinheil, Zts. Instk. 19, p. 177; 1899.

Zts. Instk. (6)

Czapski, Zts. Instk.,  6, p. 342; 1888.

Harting, Zts. Instk.1908.

Wolf: Zts. Instk.,  19, p. 1; 1899.

Harting, Zts. Instk.,  31, p. 72; 1911.

Wilsing, Zts. Instk.,  26, p. 41, 1906.

Zts. Instk.,  17, p. 50, p. 77; 1897.

Other (2)

, 1921, on “Spectral Distribution of Energy required to evoke the Gray Sensation.”

Loc. cit. p. 245.

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Figures (11)

F. 1
F. 1

Change in Focal Length with Wave Length (λ)

F. 2
F. 2

The relation between the wave length of minimum focal length (λ1) and the wave length for which the focal length becomes equal to that for the F line. Glasses: Schott 0-60 and 0-103.

F. 4
F. 4

The relation between the wave length and the intensity at the λ1-focus for α telescope objective of the size of the Lick refractor.

F. 5
F. 5

The total intensity at the λ1-focus as a function of λ1.

F. 6
F. 6

The relation between visual brightness and wave length ( V · I I 0 )

F. 7
F. 7

Comparison of the chromatic and spherical aberrations for a common type of objective of the aperture of the Lick refractor (F/19).

F. 9
F. 9

Curve AVisual brightness at the λ1-focus, λ1 = 550mμ.B0.4mm outside of the λ1-focus

F. 10
F. 10

Visual efficiency of an achromatic pair of any dimensions in terms of the parameter H 2 / F cm. Uniform spectrum and λ1-focus. Small circles, λ1 = 550mμ; large circles, λ1 = 560mμ. Glasses, ordinary crown and dense flint. The Lick objective is plotted at about 1.2 cm. The spherical aberration is assumed to be negligible.

F. 11
F. 11

Visual efficiency for a source at 6000°K. Curve 1 is for the λ1-focus, and curves 2 and 3 are for points outside the λ1-focus, for which the path difference between paraxial and peripheral rays are respectively 1 4 λ 1 and 1 2 λ 1.

Tables (4)

Tables Icon

Table 1 Chromatic Aberration of the Lick Observatory 36″ Refractor

Tables Icon

Table 2 Numerical Example of CalculationsPseudo-Lick Objectiveλ1 = 560mμ Dimensions and Constants of the LensFocal Length 57 ft.Linear Aperture 2H = 36 in. H F = 1 38 α = 1.89 1 λ · δ F F

Equations (39)

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1 / f = ( n 1 ) ( 1 / r + 1 / r )
1 / F = 1 / f + 1 / F = ( n 1 ) ( 1 / ρ ) + ( N 1 ) ( 1 / P )
1 / ρ = 1 / r + 1 / r
δ ( 1 / F ) = δ n / ρ + δ N / P
δ N δ n = P ρ
( δ F F )
n = a + b λ 2 + c λ 4 + d λ 6
n = n 0 + c ( λ λ 0 ) α
δ n = ( λ 1 λ ) c ( λ λ 0 ) ( λ 1 λ 0 )
δ N = ( λ 1 λ ) C ( λ Λ 0 ) ( λ 1 Λ 0 )
d n d λ = c ( λ 1 λ 0 ) 2 d N d λ = C ( λ 1 Λ 0 ) 2
1 F 2 · d F d λ = 1 ρ d n d λ + 1 P d N d λ = 0
c ρ 1 ( λ 1 λ 0 ) 2 = C P 1 ( λ 1 Λ 0 ) 2
1 ρ = 1 c ( λ 1 λ 0 ) 2 ( n 1 1 c ) ( λ 1 λ 0 ) 2 ( N 1 1 C ) ( λ 1 Λ 0 ) 2 × 1 F 1 P = 1 c ( λ 1 Λ 0 ) 2 ( N 1 1 C ) ( λ 1 Λ 0 ) 2 ( n 1 1 c ) ( λ 1 λ 0 ) 2 × 1 F
δ 1 F = 1 F 2 · δ F
δ F F = ( Λ 0 λ 0 ) n 1 1 c ( λ 1 λ 0 ) 2 N 1 1 C ( λ 1 Λ 0 ) 2 × ( λ λ 1 ) 2 ( λ λ 0 ) ( λ Λ 0 ) = K 1 × ( λ 1 λ ) 2 ( λ λ 0 ) ( λ Λ 0 )
d A = k · d S · cos ( θ θ 0 )
θ = 2 π ( δ λ ) = 2 π λ ( P Q P O ) = 2 π λ · P F ( 1 cos ϕ ) = π λ · P F · h 2 F Q 2
d S = 2 π h · d h = λ · F Q 2 ¯ P F · d θ
A = k · λ · F Q 2 F P [ sin ( 2 α θ 0 ) + sin θ 0 ]
A = k π h 2 sin α α
I I 0 = ( A A 0 ) 2 = ( sin α α ) 2
α = π 2 · δ F λ · ( H F ) 2
α = π 2 · 1 λ · δ F F · H 2 F
( 2 H ) 2 F = 1 or 2 H = F = 41.7 c m
d ( Δ 1 υ ) = 1 8 ρ 3 [ ( 1 2 n 2 ) s 2 + 4 ( 2 n 1 1 n 2 ) s · p + ( 9 n 2 14 n + 3 + 2 n 2 ) p 2 + ( 3 n 2 2 n ) ] H 2 · d n
s = r r r + r p = υ u υ + u
δ ( Δ 1 υ ) = 1 ρ 3 [ 0.0167 · s 1 2 + 0.803 · s 1 · p 1 + 0.820 · p 1 2 + 0.474 ] · H 2 · δ n δ ( Δ 1 υ ) = 1 P 3 ( 0.0300 · s 2 2 + 0.933 · s 2 · p 2 + 0.593 · p 2 2 + 0.583 ) · H 2 · δ N
δ ( 1 F ) = H 2 ρ 3 [ .887 δ n .765 δ N ]
H F = 1 38
α = 1.89 1 λ · δ F F
δ F F
I I 0
V · I I 0
E λ · V · I I 1
δ F F
H 2 F 2 × 0.283
( for H F = 1 38 ) + .000196
δ F F