Abstract

Astronomical refraction has had a long and fascinating history. Cleomedes (100 A.D.) and Ptolemy (200 A.D.) were aware of its existence and understood in a qualitative way some of its properties. Alhazen (1100 A.D.) quite correctly suggested that the flattening of the sun’s disk near the horizon was due to astronomical refraction. Tycho Brahe in 1587, however, was the first to make direct measurements of the magnitude of the refraction. The first theory of astronomical refraction based on Snell’s law was that of Cassini, who in 1656 looked upon the earth’s atmosphere as being of constant refractive index up to its upper limit at which all the refraction took place. Extensive investigations of the physical properties of the atmosphere modified these ideas and led to the “concentric spherical shell model” and the “plane parallel layer model,” the latter being an approximation for the former. Attempts to evaluate the “refraction integral” for the concentric spherical shell model have led to the theories of Bessel, Bradley, Gylden, Ivory, Laplace, Mayer, Simpson, Young, and others. At the beginning of the twentieth century, investigations on the physical properties of the atmosphere extended to higher elevations, and new physical properties appeared which were not anticipated by the earlier workers. This led to the celebrated work of Harzer, who for the first time was able to compute the astronomical refraction purely from meteorological measurements. Harzer also made the first detailed investigation of the applicability of the spherical shell model, which is used almost universally by workers in this field. Harzer’s work has served as a source of inspiration, but much remains to be done. This paper attempts to give a brief chronological description of some of the more significant theories of astronomical refraction for the purpose of pointing out the types of problems which have existed, how these problems were attacked, and the problems which still remain. It also gives adequate references for those wishing additional information.

© 1962 Optical Society of America

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References

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  1. C. Bruhns, Die Astronomische Strahlenbrechung in Ihrer Historischen Entwickelung, Leipzig, 1861.
  2. E. Gehrcke, Handbuch der Physikalischen Optik (Barth, Leipzig, 1927), Bd. I, p. 237.
  3. Cleomedes De Mundo, Circularis Inspectionis Meteororum (Henricum Petri, Basilae, 1585), p. 294; see ref. 1.
  4. Ptolemaeus Claudius, Opticae (Translated from Arabic to Latin by E. Sicile, reprinted by A. Lejeune, Lourain, 1956), Part V, p. 239.
  5. Alhazen, Opticae Thesaurus (Translated into the Latin by Vitello and published by F. Risner, 1572), Book VII, p. 251.
  6. Tycho Brahe’s Description of his Instruments and Scientific Work (Translated by H. Raeder, E. Stromgren, B. Stromgren, Kobenhavn, 1946).
  7. Tycho Brahe, Astronomiae Instauratae Progymnasmata (Francofurt, 1648), pp. 15, 39.
  8. E. Wilde, Geschichte der Optik (Rücker and Püchler, Berlin, 1838), Bd. I.
  9. P. Bouguer, “Sur les refractions astron. dans la zone terride,” Mém. Paris, 1739.
  10. W. Valentiner, Handwörterbuch der Astronomie (E. Trewendt, Breslau, 1901), Bd. III.
  11. E. V. Oppolzer, Sitz. Ber. Kaiserlich Akad. Wiss. (Wien, 1900) Bd. CIX, Abt. IIa, p. 578.
  12. This integral is often derived from Fermat’s law. See for example ref. 2, pp. 222–228;E. E. Kummer, “Uber Atmosphärische Strahlenbrechung,” Monatsber. kgl. Preuss. Akad. Wiss., Berlin, p. 405 (1860).
  13. Rayleigh, Phil. Mag. (5) 36 (1892); L. J. Gruey, Exercises Astronomique (Herman, Paris, 1889), p. 119; S. Newcomb, A Compendium on Spherical Astronomy (Macmillan, New York, 1906), p. 190; A. Prey, Einführung in die sphärische Astronomie (Springer, Wien, 1949).
  14. W. F. Meggers, C. G. Peters, Bull. Natl. Bur. Standards, 14, 697 (1918).
    [CrossRef]
  15. J. Bradley, Astronomical Observations at the Royal Observatory at Greenwich (Oxford, 1798), Vol. I, p. B. 1.
  16. K. Koziel, Numerikalische strenge Fassung des Laplace’s Oriani’s Satzes (Cracovie Imprimerie de L’Universite, 1931); see ref. 2, p. 249.
  17. F. W. Bessel, Fundamenta Astronomiae (Regiomonti in Commisis Apud f. Nocolovium, 1818), p. 26.
  18. F. W. Bessel, Tabulae Regiomontonae Reductionum (Black, Young, London, 1830), pp. LIX, 538.
  19. N. Bowditch, American Practical Navigator (U.S. Hydrographic Office, 1938), pp. 150–153; A. Court, J. Franklin Inst. 247, 538 (1949).
    [CrossRef]
  20. R. T. Crawford, Lick Observatory Bull. 7(6), 1907; S. Newcomb, A Compendium of Spherical Astronomy (Macmillan, New York, 1906), p. 224; C. H. Smiley, Navigation 3, 81 (1951–53); G. M. Clemence, Astron. J. 56(5), 123 (1951); G. M. Clemence, Navigation 3, 36 (1951–53).
    [CrossRef]
  21. J. Ivory, Phil. Trans. Roy. Soc., p. 437 (1823); Phil. Trans. Roy. Soc. “Bakerian Lecture,” p. 169 (1838).
  22. A. Wagner, “Die Temperatureverhältnisse in der freien Atmosphäre (Ergebnisse der internationalen Balloonaufstiege) Wien,” Beitr. Physik freien Atmosphäre, p. 57 (1910).
  23. F. J. Scrase, Nature 164, 572 (1949); Rocket Panel, Phys. Rev. 88, 1027 (1952); Etienne Vassy, Physique de L’Atmosphere (Gauthier-Villars, Paris, 1959), Tome II, Phenomenes de Refraction.
    [CrossRef] [PubMed]
  24. R. Radau, Recherches sur la Theorie des Refract. astronom. (Ann. de l’observ. deParis, Mem. XVI, 1882) p. B1.
  25. H. Gylden, Mem. Acad. Imp. Sci. St. Petersbourg (M. M. Eggers, H. Schmitzdorff, St. Petersbourg), 10, 1 (1867).
  26. Refraction Tables of Pulkovo Observatory (Acad. Sci. Press, Moscow, 1956), 4th ed.
  27. F. Link, Meteorologisches Taschenbuch (Geest & Portig, Leipzig, 1951).
  28. J. Bauschinger, “Untersuchung über die astronomische Refraktion,” Verhandl.K. B. Akad.Wiss. Munich (1896).
  29. Julius v. Hann, Lehrbuch der Meteorologie (3 Aufl. unter Mitwirkung von R. Suring, Leipzig, 1915).
  30. P. Harzer, Publikation der Sternwarte in Kiel (C. Schaidt, Kiel, 1922–24), XIII, XIV.
  31. N. Dnepprovski, “Note on Harzer’s “Refraction Tables” and their comparison with those of Pulkovo and de-Ball,” Byull. Akad. Nauk SSSR, Inst. Teoret. Astron., Leningrad (16), 177–186 (1927).
  32. F. Wunschmann, Gerlands Beitr. Geophys. 31, 83 (1931).
  33. J. E. Willis, Trans. Am. Geophys. Union II, 324 (1941).
    [CrossRef]
  34. Y. Hagihara, Japan. J. Astron. Geophys. 14, 1 (1936).
  35. C. Sugawa, Astron. Soc. Japan Publ. 7, 163 (1955).
  36. W. B. Varnum, “Differential refraction in positional astronomy,” Astron. Nachr. (5344) 223 (1925).
  37. Gustav Land, “Anomalies in astronomical refraction,” Astron. J. 59, 19 (1954).
    [CrossRef]
  38. F. Wunschmann, Die terrestrische Strahlenbrechung, E. Gehrcke, Handbuch der Physikalischen Optik (Barth, Leipzig, 1927), Bd. I, p. 273.
  39. E. van Everdingen, Anomalien der terristrischen Strahlenbrechung, E. Gehrcke, Handbuch der Physikalischen Optik (Barth, Leipzig, 1927), Bd. I, p. 282.
  40. C. Kramp, Analyse des Refrac. Astron. et Terres., Strassbourg, 1799.
  41. V. Fuss, Beobachtungen und Untersuchungen über die astronomische Strahlenbrechung, St. Petersburg, 1871.
  42. M. Kowalski, Recherches sur la Refraction astronomique, Imprimerie de l’Univ., Kasan, 1878.
  43. M. J. Mauer, Die Extinction des Fixsternlichtes in der Atmosphäre in ihrer Beziehung zur astronomischen Refraktion (D. Bürkli, Zürich, 1882).
  44. Maurice Loewy, Nouvelles Methodes pour la Determination complete de la Refraction (Gauthier-Villars, Paris, 1886, Acad. Sci. de France).
  45. A. A. Rambaut, On the Effect of Atmospheric Dispersion on the Position of a Star (Spottiswoode, London, 1895).
  46. P. H. Cowell, Bessel’s Refraction Tables arranged for Use at Royal Observatory, Greenwich (Neill, Edinburgh, 1899).
  47. A. Bemporad, “Besondere Behandlung des Einflusses der Atmosphäre,” Encycloped. Math. Wiss., LeipzigVI-2, hft. 2, 287–334 (1907).
  48. F. Nasl, J. J. Fric, “Premiere Etude sur les Anomalies de Refraction,” Bull, intern, acad. sci. Boheme, Prague (1908).
  49. Naval Observatory U.S., Dip and Refraction for Aerial Navigation, U.S. Naval Observatory Govt. Printing Office, 1916.
  50. E. A. F. W. Grossman, Untersuchungen über astron. Refraktion, München, Verlag der Königlich Bayerischen Akad. d. Wiss.1917.
  51. H. C. Plummer, “On astronomical refraction,” Monthly Notices Roy. Astron. Soc. 92, 25 (1931).
  52. Alan Fletcher, “Note on astronomical refraction,” Monthly Notices Roy. Astron. Soc. 91, 559 (1931).
  53. H. Barrell, J. E. Sears, “Refraction and dispersion of air,” Phil. Trans. Roy. Soc. London, Ser. A 238, 1–14 (1939).
    [CrossRef]
  54. F. Link, Z. Sekera, “Dioptrische Tafeln der Erdatmosphäre,” Pub. Prazske Hoezdarny, No. 14, 1–28 (1940).
  55. B. Garfinkel, “An investigation in the theory of astronomical refraction,” Astron. J. 50, 169 (1942).
    [CrossRef]
  56. E. Esclangon, “Sur les Refractions Geodesiques,” Compt. Rend., Acad. Sci. Paris, 216, 137 (1943).
  57. Axel Leijonhufvud, On Astronomic, Photographic, and Trigonometric Refraction, Dissertation, Uppsala, Stockholm, 1950.
  58. C. G. Maurice, “Astronomical refraction at great zenith distances,” Astron. J. 56(5), 123 (1951).
    [CrossRef]
  59. M. Reis, Sobra a Teoria da Refraccao Astronomica, Tipografía da Atlantida, Coimbra (1953).
  60. A. S. G. Grant, “Notes on atmospheric refractive index in Canada,” Trans. Am. Geophys. Union, 35(3), 508 (1954).
    [CrossRef]
  61. B. H. Dawson, “Formulas Sencillas para la Refraccion Astronomies,” Rev. Astron. (Buenos Aires) 28, II (139), 57 (1956).
  62. D. H. Sadler, W. A. Scott, “Refraction at low altitudes,”J. Naval Inst. London 13(2), 139 (1960).
  63. R. M. Goody, The Physics of the Stratosphere (Cambridge Univ. Press, 1958).

1960 (1)

D. H. Sadler, W. A. Scott, “Refraction at low altitudes,”J. Naval Inst. London 13(2), 139 (1960).

1956 (1)

B. H. Dawson, “Formulas Sencillas para la Refraccion Astronomies,” Rev. Astron. (Buenos Aires) 28, II (139), 57 (1956).

1955 (1)

C. Sugawa, Astron. Soc. Japan Publ. 7, 163 (1955).

1954 (2)

Gustav Land, “Anomalies in astronomical refraction,” Astron. J. 59, 19 (1954).
[CrossRef]

A. S. G. Grant, “Notes on atmospheric refractive index in Canada,” Trans. Am. Geophys. Union, 35(3), 508 (1954).
[CrossRef]

1951 (1)

C. G. Maurice, “Astronomical refraction at great zenith distances,” Astron. J. 56(5), 123 (1951).
[CrossRef]

1949 (1)

F. J. Scrase, Nature 164, 572 (1949); Rocket Panel, Phys. Rev. 88, 1027 (1952); Etienne Vassy, Physique de L’Atmosphere (Gauthier-Villars, Paris, 1959), Tome II, Phenomenes de Refraction.
[CrossRef] [PubMed]

1943 (1)

E. Esclangon, “Sur les Refractions Geodesiques,” Compt. Rend., Acad. Sci. Paris, 216, 137 (1943).

1942 (1)

B. Garfinkel, “An investigation in the theory of astronomical refraction,” Astron. J. 50, 169 (1942).
[CrossRef]

1941 (1)

J. E. Willis, Trans. Am. Geophys. Union II, 324 (1941).
[CrossRef]

1940 (1)

F. Link, Z. Sekera, “Dioptrische Tafeln der Erdatmosphäre,” Pub. Prazske Hoezdarny, No. 14, 1–28 (1940).

1939 (1)

H. Barrell, J. E. Sears, “Refraction and dispersion of air,” Phil. Trans. Roy. Soc. London, Ser. A 238, 1–14 (1939).
[CrossRef]

1936 (1)

Y. Hagihara, Japan. J. Astron. Geophys. 14, 1 (1936).

1931 (3)

F. Wunschmann, Gerlands Beitr. Geophys. 31, 83 (1931).

H. C. Plummer, “On astronomical refraction,” Monthly Notices Roy. Astron. Soc. 92, 25 (1931).

Alan Fletcher, “Note on astronomical refraction,” Monthly Notices Roy. Astron. Soc. 91, 559 (1931).

1925 (1)

W. B. Varnum, “Differential refraction in positional astronomy,” Astron. Nachr. (5344) 223 (1925).

1918 (1)

W. F. Meggers, C. G. Peters, Bull. Natl. Bur. Standards, 14, 697 (1918).
[CrossRef]

1907 (1)

R. T. Crawford, Lick Observatory Bull. 7(6), 1907; S. Newcomb, A Compendium of Spherical Astronomy (Macmillan, New York, 1906), p. 224; C. H. Smiley, Navigation 3, 81 (1951–53); G. M. Clemence, Astron. J. 56(5), 123 (1951); G. M. Clemence, Navigation 3, 36 (1951–53).
[CrossRef]

1892 (1)

Rayleigh, Phil. Mag. (5) 36 (1892); L. J. Gruey, Exercises Astronomique (Herman, Paris, 1889), p. 119; S. Newcomb, A Compendium on Spherical Astronomy (Macmillan, New York, 1906), p. 190; A. Prey, Einführung in die sphärische Astronomie (Springer, Wien, 1949).

1823 (1)

J. Ivory, Phil. Trans. Roy. Soc., p. 437 (1823); Phil. Trans. Roy. Soc. “Bakerian Lecture,” p. 169 (1838).

Alhazen,

Alhazen, Opticae Thesaurus (Translated into the Latin by Vitello and published by F. Risner, 1572), Book VII, p. 251.

Barrell, H.

H. Barrell, J. E. Sears, “Refraction and dispersion of air,” Phil. Trans. Roy. Soc. London, Ser. A 238, 1–14 (1939).
[CrossRef]

Bauschinger, J.

J. Bauschinger, “Untersuchung über die astronomische Refraktion,” Verhandl.K. B. Akad.Wiss. Munich (1896).

Bemporad, A.

A. Bemporad, “Besondere Behandlung des Einflusses der Atmosphäre,” Encycloped. Math. Wiss., LeipzigVI-2, hft. 2, 287–334 (1907).

Bessel, F. W.

F. W. Bessel, Fundamenta Astronomiae (Regiomonti in Commisis Apud f. Nocolovium, 1818), p. 26.

F. W. Bessel, Tabulae Regiomontonae Reductionum (Black, Young, London, 1830), pp. LIX, 538.

Bouguer, P.

P. Bouguer, “Sur les refractions astron. dans la zone terride,” Mém. Paris, 1739.

Bowditch, N.

N. Bowditch, American Practical Navigator (U.S. Hydrographic Office, 1938), pp. 150–153; A. Court, J. Franklin Inst. 247, 538 (1949).
[CrossRef]

Bradley, J.

J. Bradley, Astronomical Observations at the Royal Observatory at Greenwich (Oxford, 1798), Vol. I, p. B. 1.

Brahe, Tycho

Tycho Brahe, Astronomiae Instauratae Progymnasmata (Francofurt, 1648), pp. 15, 39.

Bruhns, C.

C. Bruhns, Die Astronomische Strahlenbrechung in Ihrer Historischen Entwickelung, Leipzig, 1861.

Claudius, Ptolemaeus

Ptolemaeus Claudius, Opticae (Translated from Arabic to Latin by E. Sicile, reprinted by A. Lejeune, Lourain, 1956), Part V, p. 239.

Cowell, P. H.

P. H. Cowell, Bessel’s Refraction Tables arranged for Use at Royal Observatory, Greenwich (Neill, Edinburgh, 1899).

Crawford, R. T.

R. T. Crawford, Lick Observatory Bull. 7(6), 1907; S. Newcomb, A Compendium of Spherical Astronomy (Macmillan, New York, 1906), p. 224; C. H. Smiley, Navigation 3, 81 (1951–53); G. M. Clemence, Astron. J. 56(5), 123 (1951); G. M. Clemence, Navigation 3, 36 (1951–53).
[CrossRef]

Dawson, B. H.

B. H. Dawson, “Formulas Sencillas para la Refraccion Astronomies,” Rev. Astron. (Buenos Aires) 28, II (139), 57 (1956).

De Mundo, Cleomedes

Cleomedes De Mundo, Circularis Inspectionis Meteororum (Henricum Petri, Basilae, 1585), p. 294; see ref. 1.

Dnepprovski, N.

N. Dnepprovski, “Note on Harzer’s “Refraction Tables” and their comparison with those of Pulkovo and de-Ball,” Byull. Akad. Nauk SSSR, Inst. Teoret. Astron., Leningrad (16), 177–186 (1927).

Esclangon, E.

E. Esclangon, “Sur les Refractions Geodesiques,” Compt. Rend., Acad. Sci. Paris, 216, 137 (1943).

Fletcher, Alan

Alan Fletcher, “Note on astronomical refraction,” Monthly Notices Roy. Astron. Soc. 91, 559 (1931).

Fric, J. J.

F. Nasl, J. J. Fric, “Premiere Etude sur les Anomalies de Refraction,” Bull, intern, acad. sci. Boheme, Prague (1908).

Fuss, V.

V. Fuss, Beobachtungen und Untersuchungen über die astronomische Strahlenbrechung, St. Petersburg, 1871.

Garfinkel, B.

B. Garfinkel, “An investigation in the theory of astronomical refraction,” Astron. J. 50, 169 (1942).
[CrossRef]

Gehrcke, E.

E. Gehrcke, Handbuch der Physikalischen Optik (Barth, Leipzig, 1927), Bd. I, p. 237.

Goody, R. M.

R. M. Goody, The Physics of the Stratosphere (Cambridge Univ. Press, 1958).

Grant, A. S. G.

A. S. G. Grant, “Notes on atmospheric refractive index in Canada,” Trans. Am. Geophys. Union, 35(3), 508 (1954).
[CrossRef]

Grossman, E. A. F. W.

E. A. F. W. Grossman, Untersuchungen über astron. Refraktion, München, Verlag der Königlich Bayerischen Akad. d. Wiss.1917.

Gylden, H.

H. Gylden, Mem. Acad. Imp. Sci. St. Petersbourg (M. M. Eggers, H. Schmitzdorff, St. Petersbourg), 10, 1 (1867).

Hagihara, Y.

Y. Hagihara, Japan. J. Astron. Geophys. 14, 1 (1936).

Hann, Julius v.

Julius v. Hann, Lehrbuch der Meteorologie (3 Aufl. unter Mitwirkung von R. Suring, Leipzig, 1915).

Harzer, P.

P. Harzer, Publikation der Sternwarte in Kiel (C. Schaidt, Kiel, 1922–24), XIII, XIV.

Ivory, J.

J. Ivory, Phil. Trans. Roy. Soc., p. 437 (1823); Phil. Trans. Roy. Soc. “Bakerian Lecture,” p. 169 (1838).

Kowalski, M.

M. Kowalski, Recherches sur la Refraction astronomique, Imprimerie de l’Univ., Kasan, 1878.

Koziel, K.

K. Koziel, Numerikalische strenge Fassung des Laplace’s Oriani’s Satzes (Cracovie Imprimerie de L’Universite, 1931); see ref. 2, p. 249.

Kramp, C.

C. Kramp, Analyse des Refrac. Astron. et Terres., Strassbourg, 1799.

Land, Gustav

Gustav Land, “Anomalies in astronomical refraction,” Astron. J. 59, 19 (1954).
[CrossRef]

Leijonhufvud, Axel

Axel Leijonhufvud, On Astronomic, Photographic, and Trigonometric Refraction, Dissertation, Uppsala, Stockholm, 1950.

Link, F.

F. Link, Z. Sekera, “Dioptrische Tafeln der Erdatmosphäre,” Pub. Prazske Hoezdarny, No. 14, 1–28 (1940).

F. Link, Meteorologisches Taschenbuch (Geest & Portig, Leipzig, 1951).

Loewy, Maurice

Maurice Loewy, Nouvelles Methodes pour la Determination complete de la Refraction (Gauthier-Villars, Paris, 1886, Acad. Sci. de France).

Mauer, M. J.

M. J. Mauer, Die Extinction des Fixsternlichtes in der Atmosphäre in ihrer Beziehung zur astronomischen Refraktion (D. Bürkli, Zürich, 1882).

Maurice, C. G.

C. G. Maurice, “Astronomical refraction at great zenith distances,” Astron. J. 56(5), 123 (1951).
[CrossRef]

Meggers, W. F.

W. F. Meggers, C. G. Peters, Bull. Natl. Bur. Standards, 14, 697 (1918).
[CrossRef]

Nasl, F.

F. Nasl, J. J. Fric, “Premiere Etude sur les Anomalies de Refraction,” Bull, intern, acad. sci. Boheme, Prague (1908).

Oppolzer, E. V.

E. V. Oppolzer, Sitz. Ber. Kaiserlich Akad. Wiss. (Wien, 1900) Bd. CIX, Abt. IIa, p. 578.

Peters, C. G.

W. F. Meggers, C. G. Peters, Bull. Natl. Bur. Standards, 14, 697 (1918).
[CrossRef]

Plummer, H. C.

H. C. Plummer, “On astronomical refraction,” Monthly Notices Roy. Astron. Soc. 92, 25 (1931).

Radau, R.

R. Radau, Recherches sur la Theorie des Refract. astronom. (Ann. de l’observ. deParis, Mem. XVI, 1882) p. B1.

Rambaut, A. A.

A. A. Rambaut, On the Effect of Atmospheric Dispersion on the Position of a Star (Spottiswoode, London, 1895).

Rayleigh,

Rayleigh, Phil. Mag. (5) 36 (1892); L. J. Gruey, Exercises Astronomique (Herman, Paris, 1889), p. 119; S. Newcomb, A Compendium on Spherical Astronomy (Macmillan, New York, 1906), p. 190; A. Prey, Einführung in die sphärische Astronomie (Springer, Wien, 1949).

Reis, M.

M. Reis, Sobra a Teoria da Refraccao Astronomica, Tipografía da Atlantida, Coimbra (1953).

Sadler, D. H.

D. H. Sadler, W. A. Scott, “Refraction at low altitudes,”J. Naval Inst. London 13(2), 139 (1960).

Scott, W. A.

D. H. Sadler, W. A. Scott, “Refraction at low altitudes,”J. Naval Inst. London 13(2), 139 (1960).

Scrase, F. J.

F. J. Scrase, Nature 164, 572 (1949); Rocket Panel, Phys. Rev. 88, 1027 (1952); Etienne Vassy, Physique de L’Atmosphere (Gauthier-Villars, Paris, 1959), Tome II, Phenomenes de Refraction.
[CrossRef] [PubMed]

Sears, J. E.

H. Barrell, J. E. Sears, “Refraction and dispersion of air,” Phil. Trans. Roy. Soc. London, Ser. A 238, 1–14 (1939).
[CrossRef]

Sekera, Z.

F. Link, Z. Sekera, “Dioptrische Tafeln der Erdatmosphäre,” Pub. Prazske Hoezdarny, No. 14, 1–28 (1940).

Sugawa, C.

C. Sugawa, Astron. Soc. Japan Publ. 7, 163 (1955).

Valentiner, W.

W. Valentiner, Handwörterbuch der Astronomie (E. Trewendt, Breslau, 1901), Bd. III.

van Everdingen, E.

E. van Everdingen, Anomalien der terristrischen Strahlenbrechung, E. Gehrcke, Handbuch der Physikalischen Optik (Barth, Leipzig, 1927), Bd. I, p. 282.

Varnum, W. B.

W. B. Varnum, “Differential refraction in positional astronomy,” Astron. Nachr. (5344) 223 (1925).

Wagner, A.

A. Wagner, “Die Temperatureverhältnisse in der freien Atmosphäre (Ergebnisse der internationalen Balloonaufstiege) Wien,” Beitr. Physik freien Atmosphäre, p. 57 (1910).

Wilde, E.

E. Wilde, Geschichte der Optik (Rücker and Püchler, Berlin, 1838), Bd. I.

Willis, J. E.

J. E. Willis, Trans. Am. Geophys. Union II, 324 (1941).
[CrossRef]

Wunschmann, F.

F. Wunschmann, Gerlands Beitr. Geophys. 31, 83 (1931).

F. Wunschmann, Die terrestrische Strahlenbrechung, E. Gehrcke, Handbuch der Physikalischen Optik (Barth, Leipzig, 1927), Bd. I, p. 273.

Astron. J. (3)

Gustav Land, “Anomalies in astronomical refraction,” Astron. J. 59, 19 (1954).
[CrossRef]

B. Garfinkel, “An investigation in the theory of astronomical refraction,” Astron. J. 50, 169 (1942).
[CrossRef]

C. G. Maurice, “Astronomical refraction at great zenith distances,” Astron. J. 56(5), 123 (1951).
[CrossRef]

Astron. Nachr. (1)

W. B. Varnum, “Differential refraction in positional astronomy,” Astron. Nachr. (5344) 223 (1925).

Astron. Soc. Japan Publ. (1)

C. Sugawa, Astron. Soc. Japan Publ. 7, 163 (1955).

Bull. Natl. Bur. Standards (1)

W. F. Meggers, C. G. Peters, Bull. Natl. Bur. Standards, 14, 697 (1918).
[CrossRef]

Compt. Rend., Acad. Sci. Paris (1)

E. Esclangon, “Sur les Refractions Geodesiques,” Compt. Rend., Acad. Sci. Paris, 216, 137 (1943).

Gerlands Beitr. Geophys. (1)

F. Wunschmann, Gerlands Beitr. Geophys. 31, 83 (1931).

J. Naval Inst. London (1)

D. H. Sadler, W. A. Scott, “Refraction at low altitudes,”J. Naval Inst. London 13(2), 139 (1960).

Japan. J. Astron. Geophys. (1)

Y. Hagihara, Japan. J. Astron. Geophys. 14, 1 (1936).

Lick Observatory Bull. (1)

R. T. Crawford, Lick Observatory Bull. 7(6), 1907; S. Newcomb, A Compendium of Spherical Astronomy (Macmillan, New York, 1906), p. 224; C. H. Smiley, Navigation 3, 81 (1951–53); G. M. Clemence, Astron. J. 56(5), 123 (1951); G. M. Clemence, Navigation 3, 36 (1951–53).
[CrossRef]

Monthly Notices Roy. Astron. Soc. (2)

H. C. Plummer, “On astronomical refraction,” Monthly Notices Roy. Astron. Soc. 92, 25 (1931).

Alan Fletcher, “Note on astronomical refraction,” Monthly Notices Roy. Astron. Soc. 91, 559 (1931).

Nature (1)

F. J. Scrase, Nature 164, 572 (1949); Rocket Panel, Phys. Rev. 88, 1027 (1952); Etienne Vassy, Physique de L’Atmosphere (Gauthier-Villars, Paris, 1959), Tome II, Phenomenes de Refraction.
[CrossRef] [PubMed]

Phil. Mag. (1)

Rayleigh, Phil. Mag. (5) 36 (1892); L. J. Gruey, Exercises Astronomique (Herman, Paris, 1889), p. 119; S. Newcomb, A Compendium on Spherical Astronomy (Macmillan, New York, 1906), p. 190; A. Prey, Einführung in die sphärische Astronomie (Springer, Wien, 1949).

Phil. Trans. Roy. Soc. (1)

J. Ivory, Phil. Trans. Roy. Soc., p. 437 (1823); Phil. Trans. Roy. Soc. “Bakerian Lecture,” p. 169 (1838).

Phil. Trans. Roy. Soc. London, Ser. A (1)

H. Barrell, J. E. Sears, “Refraction and dispersion of air,” Phil. Trans. Roy. Soc. London, Ser. A 238, 1–14 (1939).
[CrossRef]

Pub. Prazske Hoezdarny (1)

F. Link, Z. Sekera, “Dioptrische Tafeln der Erdatmosphäre,” Pub. Prazske Hoezdarny, No. 14, 1–28 (1940).

Rev. Astron. (Buenos Aires) (1)

B. H. Dawson, “Formulas Sencillas para la Refraccion Astronomies,” Rev. Astron. (Buenos Aires) 28, II (139), 57 (1956).

Trans. Am. Geophys. Union (1)

A. S. G. Grant, “Notes on atmospheric refractive index in Canada,” Trans. Am. Geophys. Union, 35(3), 508 (1954).
[CrossRef]

Trans. Am. Geophys. Union II (1)

J. E. Willis, Trans. Am. Geophys. Union II, 324 (1941).
[CrossRef]

Other (42)

A. Wagner, “Die Temperatureverhältnisse in der freien Atmosphäre (Ergebnisse der internationalen Balloonaufstiege) Wien,” Beitr. Physik freien Atmosphäre, p. 57 (1910).

J. Bradley, Astronomical Observations at the Royal Observatory at Greenwich (Oxford, 1798), Vol. I, p. B. 1.

K. Koziel, Numerikalische strenge Fassung des Laplace’s Oriani’s Satzes (Cracovie Imprimerie de L’Universite, 1931); see ref. 2, p. 249.

F. W. Bessel, Fundamenta Astronomiae (Regiomonti in Commisis Apud f. Nocolovium, 1818), p. 26.

F. W. Bessel, Tabulae Regiomontonae Reductionum (Black, Young, London, 1830), pp. LIX, 538.

N. Bowditch, American Practical Navigator (U.S. Hydrographic Office, 1938), pp. 150–153; A. Court, J. Franklin Inst. 247, 538 (1949).
[CrossRef]

F. Wunschmann, Die terrestrische Strahlenbrechung, E. Gehrcke, Handbuch der Physikalischen Optik (Barth, Leipzig, 1927), Bd. I, p. 273.

E. van Everdingen, Anomalien der terristrischen Strahlenbrechung, E. Gehrcke, Handbuch der Physikalischen Optik (Barth, Leipzig, 1927), Bd. I, p. 282.

C. Kramp, Analyse des Refrac. Astron. et Terres., Strassbourg, 1799.

V. Fuss, Beobachtungen und Untersuchungen über die astronomische Strahlenbrechung, St. Petersburg, 1871.

M. Kowalski, Recherches sur la Refraction astronomique, Imprimerie de l’Univ., Kasan, 1878.

M. J. Mauer, Die Extinction des Fixsternlichtes in der Atmosphäre in ihrer Beziehung zur astronomischen Refraktion (D. Bürkli, Zürich, 1882).

Maurice Loewy, Nouvelles Methodes pour la Determination complete de la Refraction (Gauthier-Villars, Paris, 1886, Acad. Sci. de France).

A. A. Rambaut, On the Effect of Atmospheric Dispersion on the Position of a Star (Spottiswoode, London, 1895).

P. H. Cowell, Bessel’s Refraction Tables arranged for Use at Royal Observatory, Greenwich (Neill, Edinburgh, 1899).

A. Bemporad, “Besondere Behandlung des Einflusses der Atmosphäre,” Encycloped. Math. Wiss., LeipzigVI-2, hft. 2, 287–334 (1907).

F. Nasl, J. J. Fric, “Premiere Etude sur les Anomalies de Refraction,” Bull, intern, acad. sci. Boheme, Prague (1908).

Naval Observatory U.S., Dip and Refraction for Aerial Navigation, U.S. Naval Observatory Govt. Printing Office, 1916.

E. A. F. W. Grossman, Untersuchungen über astron. Refraktion, München, Verlag der Königlich Bayerischen Akad. d. Wiss.1917.

R. Radau, Recherches sur la Theorie des Refract. astronom. (Ann. de l’observ. deParis, Mem. XVI, 1882) p. B1.

H. Gylden, Mem. Acad. Imp. Sci. St. Petersbourg (M. M. Eggers, H. Schmitzdorff, St. Petersbourg), 10, 1 (1867).

Refraction Tables of Pulkovo Observatory (Acad. Sci. Press, Moscow, 1956), 4th ed.

F. Link, Meteorologisches Taschenbuch (Geest & Portig, Leipzig, 1951).

J. Bauschinger, “Untersuchung über die astronomische Refraktion,” Verhandl.K. B. Akad.Wiss. Munich (1896).

Julius v. Hann, Lehrbuch der Meteorologie (3 Aufl. unter Mitwirkung von R. Suring, Leipzig, 1915).

P. Harzer, Publikation der Sternwarte in Kiel (C. Schaidt, Kiel, 1922–24), XIII, XIV.

N. Dnepprovski, “Note on Harzer’s “Refraction Tables” and their comparison with those of Pulkovo and de-Ball,” Byull. Akad. Nauk SSSR, Inst. Teoret. Astron., Leningrad (16), 177–186 (1927).

C. Bruhns, Die Astronomische Strahlenbrechung in Ihrer Historischen Entwickelung, Leipzig, 1861.

E. Gehrcke, Handbuch der Physikalischen Optik (Barth, Leipzig, 1927), Bd. I, p. 237.

Cleomedes De Mundo, Circularis Inspectionis Meteororum (Henricum Petri, Basilae, 1585), p. 294; see ref. 1.

Ptolemaeus Claudius, Opticae (Translated from Arabic to Latin by E. Sicile, reprinted by A. Lejeune, Lourain, 1956), Part V, p. 239.

Alhazen, Opticae Thesaurus (Translated into the Latin by Vitello and published by F. Risner, 1572), Book VII, p. 251.

Tycho Brahe’s Description of his Instruments and Scientific Work (Translated by H. Raeder, E. Stromgren, B. Stromgren, Kobenhavn, 1946).

Tycho Brahe, Astronomiae Instauratae Progymnasmata (Francofurt, 1648), pp. 15, 39.

E. Wilde, Geschichte der Optik (Rücker and Püchler, Berlin, 1838), Bd. I.

P. Bouguer, “Sur les refractions astron. dans la zone terride,” Mém. Paris, 1739.

W. Valentiner, Handwörterbuch der Astronomie (E. Trewendt, Breslau, 1901), Bd. III.

E. V. Oppolzer, Sitz. Ber. Kaiserlich Akad. Wiss. (Wien, 1900) Bd. CIX, Abt. IIa, p. 578.

This integral is often derived from Fermat’s law. See for example ref. 2, pp. 222–228;E. E. Kummer, “Uber Atmosphärische Strahlenbrechung,” Monatsber. kgl. Preuss. Akad. Wiss., Berlin, p. 405 (1860).

R. M. Goody, The Physics of the Stratosphere (Cambridge Univ. Press, 1958).

Axel Leijonhufvud, On Astronomic, Photographic, and Trigonometric Refraction, Dissertation, Uppsala, Stockholm, 1950.

M. Reis, Sobra a Teoria da Refraccao Astronomica, Tipografía da Atlantida, Coimbra (1953).

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Figures (7)

Fig. 1
Fig. 1

Tycho Brahe’s method for detecting the presence of astronomical refraction.

Fig. 2
Fig. 2

Cassini’s model for astronomical refraction.

Fig. 3
Fig. 3

The concentric spherical shell model for astronomical refraction.

Fig. 4
Fig. 4

The plane parallel layer model for astronomical refraction.

Fig. 5
Fig. 5

Computed astronomical refraction as a function of latitude obtained from the Pulkovo tables.

Fig. 6
Fig. 6

Two-dimensional plot of Harzer’s optical surfaces over Kiel, Germany.

Fig. 7
Fig. 7

Computed astronomical refraction as a function of time of year obtained from Sugawa’s theory.

Tables (7)

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Table I Brahe’s Measured Astronomical Refraction on the Sun for Different Apparent Zenith Angles

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Table II Cassini’s Computed Astronomical Refraction for Different Apparent Zenith Angles

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Table III Comparison between Computed Astronomical Refraction at Different Apparent Zenith Angles for the Plane Parallel Layer Model and the Concentric Spherical Shell Model

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Table IV Schmidt’s Model of the Earth’s Atmosphere

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Table V Computed Astronomical Refractions for Different Apparent Zenith Angles, and Temperature Corrections from Theories of Laplace, Ivory, and Schmidt

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Table VI Computed Astronomical Refractions for Different Apparent Zenith Angles from the Theories of Harzer, Gylden, and Radan

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Table VII Astronomical Refractions at Different Apparent Zenith Angles for Different Regions of the Atmosphere from Wunschmann’s Computations

Equations (30)

Equations on this page are rendered with MathJax. Learn more.

sin i 1 = sin ( e 1 + R 1 ) = μ sin e 1 , sin i 2 = sin ( e 2 + R 2 ) = μ sin e 2 ,
sin e 1 a = sin Z 1 a + H , sin e 2 a = sin Z 2 a + H .
μ n sin i n = μ n + 1 sin e n .
sin e n r n + 1 = sin i n + 1 r n .
μ n r n sin i n = μ n + 1 r n + 1 sin i n + 1 = μ e a sin Z .
d i = tan i d μ μ tan i d r r .
z i 0 d i = μ e μ s tan i d μ μ 0 ω 0 d ω ,
R = ( Z 0 Z ) = μ s μ e μ e a sin Z μ 2 ( a + h ) 2 μ e 2 a 2 sin 2 Z d μ μ ( i 0 θ ) .
( i 0 θ ) = a r ( μ e sin Z sin Z 0 ) .
( i 0 θ ) = a r s sin Z [ ( μ e 1 ) R cos Z + R 2 2 ] .
R = 1 μ e μ e a sin Z μ 2 ( a + h ) 2 μ e 2 a 2 sin 2 Z d μ μ .
μ s sin i s = μ n sin i n = μ e sin Z ,
sin R = μ e μ s sin Z cos ( Z + θ s ) × [ 1 1 μ e 2 sin 2 Z μ s 2 sin 2 ( Z + θ s ) μ e 2 sin 2 Z cos 2 ( Z + θ s ) ] .
sin R = μ e sin 2 Z 2 [ 1 1 μ e 2 1 μ e 2 cos 2 Z ] .
R = ( μ e 1 ) tan Z + ( μ e 1 ) 2 2 tan 3 Z + ( μ e 1 ) 3 2 tan 5 Z +
μ = μ e ( a a + h ) 1 / ( m + 1 ) ,
R = 1 m [ Z arc sin ( sin Z μ e m ) ] ,
R = ( μ e 1 ) tan ( Z m R 2 ) ,
ρ ρ 0 = P P 0 ( 1 + β t ) ,
μ 2 = 1 + 2 C ,
d P = g e [ a / ( a + h ) ] 2 d h .
R = ( μ e 1 ) [ ( 1 + μ e 1 2 ) tan Z ( l e a μ e 1 2 ) tan 3 Z ] .
R = 60.3826 tan Z 57.9953 × 10 3 tan 3 Z .
R = α ( B T ) A γ λ tan Z .
1 + β t 1 β t e = 1 f ( 1 ρ ρ e ) ,
1 + β t 1 β t e = 1 h H e ,
1 + β t 1 + β t e = ( 1 1 2 m h a + H ) 2 ,
R = α ( B T ) A γ λ tan Z ( C · D · E ) .
R = tan Z 1 μ h d μ μ = log e μ h · tan Z .
( μ 1 ) = γ P γ ( μ γ 0 1 ) P 0 ( 1 + α t ) ,

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