Abstract

The history of ideas on the blue of the sky, the rainbow, and the visibility of distant objects is briefly sketched. In particular, it is shown that the theory of the horizontal visual range was largely rediscovered after about 175 years.

© 1960 Optical Society of America

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References

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  1. L. da Vinci, Trattato della pittura, quoted by Pernter and Exner, Meteorologische Optik (1922), second edition, p. 614.
  2. H. B. de Saussure, Mem. Acad. Turin 4, 409–424 (1789).
  3. J. Chappuis, Compt. rend. 91, 985–986 (1880).
  4. E. O. Hulburt, J. Opt. Soc. Am. 43, 113–118 (1953).
    [Crossref]
  5. R. Clausius, Ann. Physik 16, 161–188 (1849).
    [Crossref]
  6. I. Newton, Opticks (1704), Book  II, Pt. 3, Prop. 7.
  7. J. Tyndall, Proc. Roy. Soc. London 17, 223–233 (1869).
  8. J. D. Forbes, Trans. Roy. Soc. Edinburgh 14, 371–374 (1840).
    [Crossref]
  9. J. D. Forbes, Trans. Roy. Soc. Edinburgh 14, 375–391 (1840).
    [Crossref]
  10. Rayleigh, Phil. Mag. 41, 107–120, 274–279 (1871), and many other papers. See Rayleigh, Collected Works.
  11. S. Chandrasekhar, Radiative Transfer (Clarendon Press, Oxford, 1950).
  12. W. Ostwald and F. Linke, Meteorol. Z. 45, 367–370 (1928).
  13. I. G. Priest, J. Opt. Soc. Am. 7, 1175–1209 (1923).
    [Crossref]
  14. For a very extensive history of man’s ideas about the rainbow, see C. B. Boyer, The Rainbow from Myth to Mathematics (Thomas Yoseleff, New York and London, 1959).
  15. A. M. Sayeli, Isis 30, 65–83 (1939).
    [Crossref]
  16. J. F. Scott, The Scientific Work of Réné Descartes (Taylor and Francis, London), n.d.
  17. Roger Bacon, Opus Majus, translated by R. B. Burke (University of Pennsylvania Press, Philadelphia, 1928), Vol. 1, P. 235.
  18. See reference 17, Vol. 2, p. 592 ff.
  19. G. Sarton, Introduction to the History of Science, Vol.  III, Pt. i, p. 706.
  20. For a good account see reference 14, p. 110 ff.
  21. Descartes, Les Méteores, in Oeuvres de Descartes, VI, edited by Adam and Tannery, (Paris, 1897–1913), 12 Vols. and Suppl.
  22. See reference 6, Book I, Pt. 2, Prop. 9.
  23. T. Young, Phil. Trans. Roy. Soc. London 92, 387–397 (1802).
    [Crossref]
  24. G. B. Airy, Trans. Cambridge Phil. Soc. 6, 379–403 (1838).
  25. For example, W. H. Miller, Trans. Cambridge Phil. Soc. 70, 277–286 (1842).
  26. (a)P. Bouguer, Essai d’Optique sur la gradation de la lumière (Paris, 1729). (b)Traite d’Optique sur la gradation de la lumière, posthumous, edited by N. L. de la Caille (Paris, 1760).
  27. See F. Perrin, J. Opt. Soc. Am. 38, 72–74 (1948).
    [Crossref] [PubMed]
  28. See reference 26 (b), p. 82.
  29. See reference 26(b), p. 265 ff.
  30. E. Allard, Memoire sur l’intensité et la portée des phares (Dunod, Paris, 1876).
  31. Reference 26(b), p. 360.
  32. There were 20 leagues to the degree of latitude.
  33. The italics are mine. In view of the importance of this point, I give the original, “Mais si l’atmosphere est bien serein, la montagne sera couverte de toute la lumière aérienne renvoyée par la masse d’air comprise entre l’objet et l’oeil de l’observateur; et cette couleur sera exprimée par (2525/10000)q, pendant que celle de toute l’atmosphere, ou celle du ciel qu’on verra à côté, le sera par (2575/10000)q.”
  34. H. Koschmieder, Beitr. Phys. freien Atmos. 12, 33–53 and 171–181 (1924).
  35. J. H. Lambert, Mem. Acad. Berlin, 74–80 (1774).
  36. M. Hugon, Sci. et ind. phot. 1, 161–168, 201–212 (1930). S. Q. Duntley, J. Opt. Soc. Am. 38, 179–191 (1948).
    [Crossref]
  37. H. B. de Saussure, Mem. Acad. Turin 4, 425–440 (1789).

1953 (1)

1948 (1)

1939 (1)

A. M. Sayeli, Isis 30, 65–83 (1939).
[Crossref]

1930 (1)

M. Hugon, Sci. et ind. phot. 1, 161–168, 201–212 (1930). S. Q. Duntley, J. Opt. Soc. Am. 38, 179–191 (1948).
[Crossref]

1928 (1)

W. Ostwald and F. Linke, Meteorol. Z. 45, 367–370 (1928).

1924 (1)

H. Koschmieder, Beitr. Phys. freien Atmos. 12, 33–53 and 171–181 (1924).

1923 (1)

1880 (1)

J. Chappuis, Compt. rend. 91, 985–986 (1880).

1871 (1)

Rayleigh, Phil. Mag. 41, 107–120, 274–279 (1871), and many other papers. See Rayleigh, Collected Works.

1869 (1)

J. Tyndall, Proc. Roy. Soc. London 17, 223–233 (1869).

1849 (1)

R. Clausius, Ann. Physik 16, 161–188 (1849).
[Crossref]

1842 (1)

For example, W. H. Miller, Trans. Cambridge Phil. Soc. 70, 277–286 (1842).

1840 (2)

J. D. Forbes, Trans. Roy. Soc. Edinburgh 14, 371–374 (1840).
[Crossref]

J. D. Forbes, Trans. Roy. Soc. Edinburgh 14, 375–391 (1840).
[Crossref]

1838 (1)

G. B. Airy, Trans. Cambridge Phil. Soc. 6, 379–403 (1838).

1802 (1)

T. Young, Phil. Trans. Roy. Soc. London 92, 387–397 (1802).
[Crossref]

1789 (2)

H. B. de Saussure, Mem. Acad. Turin 4, 425–440 (1789).

H. B. de Saussure, Mem. Acad. Turin 4, 409–424 (1789).

1774 (1)

J. H. Lambert, Mem. Acad. Berlin, 74–80 (1774).

1704 (1)

I. Newton, Opticks (1704), Book  II, Pt. 3, Prop. 7.

Airy, G. B.

G. B. Airy, Trans. Cambridge Phil. Soc. 6, 379–403 (1838).

Allard, E.

E. Allard, Memoire sur l’intensité et la portée des phares (Dunod, Paris, 1876).

Bacon, Roger

Roger Bacon, Opus Majus, translated by R. B. Burke (University of Pennsylvania Press, Philadelphia, 1928), Vol. 1, P. 235.

Bouguer, P.

(a)P. Bouguer, Essai d’Optique sur la gradation de la lumière (Paris, 1729). (b)Traite d’Optique sur la gradation de la lumière, posthumous, edited by N. L. de la Caille (Paris, 1760).

Boyer, C. B.

For a very extensive history of man’s ideas about the rainbow, see C. B. Boyer, The Rainbow from Myth to Mathematics (Thomas Yoseleff, New York and London, 1959).

Chandrasekhar, S.

S. Chandrasekhar, Radiative Transfer (Clarendon Press, Oxford, 1950).

Chappuis, J.

J. Chappuis, Compt. rend. 91, 985–986 (1880).

Clausius, R.

R. Clausius, Ann. Physik 16, 161–188 (1849).
[Crossref]

da Vinci, L.

L. da Vinci, Trattato della pittura, quoted by Pernter and Exner, Meteorologische Optik (1922), second edition, p. 614.

de Saussure, H. B.

H. B. de Saussure, Mem. Acad. Turin 4, 409–424 (1789).

H. B. de Saussure, Mem. Acad. Turin 4, 425–440 (1789).

Descartes,

Descartes, Les Méteores, in Oeuvres de Descartes, VI, edited by Adam and Tannery, (Paris, 1897–1913), 12 Vols. and Suppl.

Forbes, J. D.

J. D. Forbes, Trans. Roy. Soc. Edinburgh 14, 371–374 (1840).
[Crossref]

J. D. Forbes, Trans. Roy. Soc. Edinburgh 14, 375–391 (1840).
[Crossref]

Hugon, M.

M. Hugon, Sci. et ind. phot. 1, 161–168, 201–212 (1930). S. Q. Duntley, J. Opt. Soc. Am. 38, 179–191 (1948).
[Crossref]

Hulburt, E. O.

Koschmieder, H.

H. Koschmieder, Beitr. Phys. freien Atmos. 12, 33–53 and 171–181 (1924).

Lambert, J. H.

J. H. Lambert, Mem. Acad. Berlin, 74–80 (1774).

Linke, F.

W. Ostwald and F. Linke, Meteorol. Z. 45, 367–370 (1928).

Miller, W. H.

For example, W. H. Miller, Trans. Cambridge Phil. Soc. 70, 277–286 (1842).

Newton, I.

I. Newton, Opticks (1704), Book  II, Pt. 3, Prop. 7.

Ostwald, W.

W. Ostwald and F. Linke, Meteorol. Z. 45, 367–370 (1928).

Perrin, F.

Priest, I. G.

Rayleigh,

Rayleigh, Phil. Mag. 41, 107–120, 274–279 (1871), and many other papers. See Rayleigh, Collected Works.

Sarton, G.

G. Sarton, Introduction to the History of Science, Vol.  III, Pt. i, p. 706.

Sayeli, A. M.

A. M. Sayeli, Isis 30, 65–83 (1939).
[Crossref]

Scott, J. F.

J. F. Scott, The Scientific Work of Réné Descartes (Taylor and Francis, London), n.d.

Tyndall, J.

J. Tyndall, Proc. Roy. Soc. London 17, 223–233 (1869).

Young, T.

T. Young, Phil. Trans. Roy. Soc. London 92, 387–397 (1802).
[Crossref]

Ann. Physik (1)

R. Clausius, Ann. Physik 16, 161–188 (1849).
[Crossref]

Beitr. Phys. freien Atmos. (1)

H. Koschmieder, Beitr. Phys. freien Atmos. 12, 33–53 and 171–181 (1924).

Compt. rend. (1)

J. Chappuis, Compt. rend. 91, 985–986 (1880).

Introduction to the History of Science (1)

G. Sarton, Introduction to the History of Science, Vol.  III, Pt. i, p. 706.

Isis (1)

A. M. Sayeli, Isis 30, 65–83 (1939).
[Crossref]

J. Opt. Soc. Am. (3)

Mem. Acad. Berlin (1)

J. H. Lambert, Mem. Acad. Berlin, 74–80 (1774).

Mem. Acad. Turin (2)

H. B. de Saussure, Mem. Acad. Turin 4, 425–440 (1789).

H. B. de Saussure, Mem. Acad. Turin 4, 409–424 (1789).

Meteorol. Z. (1)

W. Ostwald and F. Linke, Meteorol. Z. 45, 367–370 (1928).

Opticks (1)

I. Newton, Opticks (1704), Book  II, Pt. 3, Prop. 7.

Phil. Mag. (1)

Rayleigh, Phil. Mag. 41, 107–120, 274–279 (1871), and many other papers. See Rayleigh, Collected Works.

Phil. Trans. Roy. Soc. London (1)

T. Young, Phil. Trans. Roy. Soc. London 92, 387–397 (1802).
[Crossref]

Proc. Roy. Soc. London (1)

J. Tyndall, Proc. Roy. Soc. London 17, 223–233 (1869).

Sci. et ind. phot. (1)

M. Hugon, Sci. et ind. phot. 1, 161–168, 201–212 (1930). S. Q. Duntley, J. Opt. Soc. Am. 38, 179–191 (1948).
[Crossref]

Trans. Cambridge Phil. Soc. (2)

G. B. Airy, Trans. Cambridge Phil. Soc. 6, 379–403 (1838).

For example, W. H. Miller, Trans. Cambridge Phil. Soc. 70, 277–286 (1842).

Trans. Roy. Soc. Edinburgh (2)

J. D. Forbes, Trans. Roy. Soc. Edinburgh 14, 371–374 (1840).
[Crossref]

J. D. Forbes, Trans. Roy. Soc. Edinburgh 14, 375–391 (1840).
[Crossref]

Other (16)

L. da Vinci, Trattato della pittura, quoted by Pernter and Exner, Meteorologische Optik (1922), second edition, p. 614.

S. Chandrasekhar, Radiative Transfer (Clarendon Press, Oxford, 1950).

For a very extensive history of man’s ideas about the rainbow, see C. B. Boyer, The Rainbow from Myth to Mathematics (Thomas Yoseleff, New York and London, 1959).

J. F. Scott, The Scientific Work of Réné Descartes (Taylor and Francis, London), n.d.

Roger Bacon, Opus Majus, translated by R. B. Burke (University of Pennsylvania Press, Philadelphia, 1928), Vol. 1, P. 235.

See reference 17, Vol. 2, p. 592 ff.

(a)P. Bouguer, Essai d’Optique sur la gradation de la lumière (Paris, 1729). (b)Traite d’Optique sur la gradation de la lumière, posthumous, edited by N. L. de la Caille (Paris, 1760).

For a good account see reference 14, p. 110 ff.

Descartes, Les Méteores, in Oeuvres de Descartes, VI, edited by Adam and Tannery, (Paris, 1897–1913), 12 Vols. and Suppl.

See reference 6, Book I, Pt. 2, Prop. 9.

See reference 26 (b), p. 82.

See reference 26(b), p. 265 ff.

E. Allard, Memoire sur l’intensité et la portée des phares (Dunod, Paris, 1876).

Reference 26(b), p. 360.

There were 20 leagues to the degree of latitude.

The italics are mine. In view of the importance of this point, I give the original, “Mais si l’atmosphere est bien serein, la montagne sera couverte de toute la lumière aérienne renvoyée par la masse d’air comprise entre l’objet et l’oeil de l’observateur; et cette couleur sera exprimée par (2525/10000)q, pendant que celle de toute l’atmosphere, ou celle du ciel qu’on verra à côté, le sera par (2575/10000)q.”

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