Abstract
Early one morning in 1735, a small group of people were gathered on top of a mountain in the Peruvian Andes. They belonged to a French scientific expedition, led by Bouguer and La Condamine, that had been sent out to measure a degree of longitude; a Spanish captain named Antonio de Ulloa accompanied them. What they saw on this occasion was, according to Bouguer [1]9 “a phenomenon which must be as old as the world, but which no one seems to have observed so far… A cloud that covered us dissolved itself and let through the rays of the rising sun… Then each of us saw his shadow projected upon the cloud… The closeness of the shadow allowed all its parts to be distinguished: arms, legs, the head. What seemed most remarkable to us was the appearance of a halo or glory around the head, consisting of three or four small concentric circles, very brightly colored, each of them with the same colors as the primary rainbow, with red outermost…”. Ulloa, who gave a similar decription and also drew a picture of what he observed, added: “The most surprising thing was that, of the six or seven people that were present, each one saw the phenomenon only around the shadow of his own head, and saw nothing around other people’s heads…”
Work partially supported by the National Research Council of Brazil.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References and Footnotes
J. M. Pernter and F. M. Exner, “Meteorologische Optik”,(W. Braumiiller, Vienna, 1910).
A. Hayter “A Voyage in Vain: Coleridge’s Journey to Malta in 1804”,(Faber and Faber, London, 1973). We are indebted to Professor J. B. French for this reference.
“The Autobiography of Benvenuto Cellini”,(Brentano’s, New York, 1906), Chapter 128.
R. A. R. Tricker, “Introduction to Meteorological Optics”,( American Elsevier Publishing Co., New York, 1970).
J. C. Brandt, Publ. Astron. Soc. Pacific 80, 25(1968)
H. C. Bryant and N. Jarmie, Scient. Amer., 231, 60(July 1974).
C. T. R. Wilson, Nobel Prize Lecture(1927).
H. C. Van de Hulst, “Light Scattering by Small Particles”,( John Wiley and Sons, New York, 1957).
G. Mie, Ann. Physik, 25, 377(1908).
V. Khare and H. M. Nussenzveig,(to be published).
B. Ray, Nature 111, 183(1923).
H. M. Nussenzveig, J. Math. Phys., 10, 82, 125(1969).
H. C. Bryant and A. J. Cox, J. Opt. Soc. Am., 56, 1529(1966).
J. Bricard, Ann. Physique 14, 148(1940)
J. Bricard, Handb. d. Phys., 48, 351,( Springer-Verlag, Berlin, 1957).
H. Bucerius, Optik, 1, 188(1946).
H. C. Van de Hulst, J. Opt. Soc. Am., 37, 16(1947); see also ref. 7.
H. Ott, Ann. Physik, 41, 443(1942); 4, 432(1948).
T. S. Fahlen and H. C. Bryant, J. Opt. Soc. Am., 58, 304(1968).
J. V. Dave, Appl. Opt., 8, 155(1969).
M. J. Saunders, J. Opt. Soc. Am., 60, 1359(1970).
For the early history of this subject, see N. A. Logan Proc. IEEE, 53, 773(1965).
V. A. Fock, “Diffraction of Radio Waves Around the Earth’s Surface”,( Publishers of the USSR Academy of Sciences, Moscow, 1946).
H. Bremmer, “Terrestrial Radio Waves”,( Elsevier, New York, 1949).
B. Van der Pol and H. Bremmer, Phil. Mag., 24, 141, 825(1937).
W. Franz, “Theorie der Beugung Elektromagnetischer Wellen”,( Springer-Verlag, Berlin, 1957).
S. I. Rubinow, Ann. Phys.(N.Y.) 14, 305(1961).
H. M. Nussenzveig, Ann. Phys.(N.Y.) 34, 23(1965).
V. Khare, Ph.D. Thesis, University of Rochester(1975)
V. Khare and H. M. Nussenzveig,(to be published).
V. Khare and H. M. Nussenzveig, Phys. Rev. Lett., 33, 976(1974).
H. M. Nussenzveig, in “Methods and Problems of Theoret ical Physics”, J. E. Bowcock ed.,( North-Holland Publishing Co., Amsterdam, 1970), p. 203.
E. C. Titchmarsh, “Introduction to the Theory of Fourier Integrals”, 2nd ed.,(Oxford University Press 1937), p. 60.
M. V. Berry and K. E. Mount, Rep. Prog. Phys., 35, 315(1972).
J. B. Keller, in Proc. Symp. Appl. Math., Vol. 8, L. M. Graves ed.,(McGraw-Hill, New York, 1958), p. 27.
P. J. Debye, Physik. Z., 9, 775(1908).
K. W. Ford, D. L. Hill, M. Wakano and J. A. Wheeler, Ann. Phys.(N.Y.) 7, 239(1959).
C. Chester, B. Friedman and F. Ursell, Proc. Camb. Phil. Soc., 53, 599(1957)
F. Ursell, Proc. Camb. Phil. Soc., 61, 113(1965).
H. M. Nussenzveig, Scient. Amer., 236, 116(April 1977)
T. S. Fahlen and H. C. Bryant, J. Opt. Soc. Am., 56, 1635(1966).
A. Sommerfeld, “Optics”,( Academic Press Inc., New York, 1954), p. 262.
The direct-reflection term p = 0 is omitted in all curves. This does not affect the comparison.
P. Walstra, Proc. Koninkl. Akad. Wetensch., B67, 491(1964).
M. A. D. Fluendy and K. P. Lawley, “Chemical Applications of Molecular Beam Scattering”,( Chapman and Hall, London, 1973).
M. V. Berry, J. Phys., B2, 381(1969).
H. L. Harney, P. Braun-Munzinger and C. K. Gelbke, eds. “Classical and Quantum-Mechanical Aspects of Heavy- Ion Collisions”,(Springer-Verlag, Berlin, 1975); cf. specially the contributions by W. E. Frahn and K. W. McVoy and the references quoted therein.
W. H. Miller, Adv. Chem. Phys., 25, 63(1974)
T. F. George and J. Ross, Ann. Rev. Phys. Chem., 24, 263(1973).
C. G. Callan, Jr., R. F. Dashen and D. J. Gross, Phys. Lett., 63B, 334(1976).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1977 Plenum Press, New York
About this chapter
Cite this chapter
Khare, V., Nussenzveig, H.M. (1977). The Theory of the Glory. In: Landman, U. (eds) Statistical Mechanics and Statistical Methods in Theory and Application. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-4166-6_31
Download citation
DOI: https://doi.org/10.1007/978-1-4613-4166-6_31
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4613-4168-0
Online ISBN: 978-1-4613-4166-6
eBook Packages: Springer Book Archive