Abstract

A computer simulation technique is used to investigate the origins of the arcs of Lowitz. The model explored consists of light passing through a hexagonal ice plate, spinning about a major diagonal axis that remains horizontal as the crystal falls.

© 1979 Optical Society of America

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References

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  1. T. Lowitz, Nova Acta Acad. Imp. Sc. Petropol 8, 384 (1794).(Although the account was published in 1794, the observation of the St. Petersburg complex was actually made on June 18, 1790, not July 1794 as reported in Refs. 5 and 7.)
  2. W. Evans and R. A. R. Tricker, Weather 27, 234 (1972);R. A. R. Tricker, Weather 25, 502 (1970);ibid. 28, 159 (1973);P. P. Hattinga Verschure, Weather 26, 532 (1971);ibid. 28, 300 (1973);R. E. Lacy, M. A. Ellison, and S. E. Ashmore, Weather 9, 206 (1954);G. W. Robertson, Weather 29, 113 (1974);R. Scutt, Weather 23, 525 (1968).
    [Crossref]
  3. R. D. Edge, Am. J. Phys. 44, 780 (1976).
    [Crossref]
  4. J. M. Pernter and F. M. Exner, Meteorologische Optik, 2nd ed. (Vienna and Leipzig, 1922).
  5. W. J. Humphreys, Physics of the Air, (republication by Dover, 1964,Physics of the Air of the 3rd edition published by McGraw-Hill, New York, 1940).
  6. S. Fujiwhara and S. Oti, Bull. Cent. Met. Obs. Japan III, 33 (1919).
  7. R. A. R. Tricker, Introduction to Meteorological Optics (American Elsevier, New York, 1970).
  8. R. A. R. Tricker, Q. J. R. Meteorol. Soc. 98, 542 (1972).
  9. R. G. Greenler and A. J. Mallmann, Science 176, 128 (1972).
    [Crossref] [PubMed]
  10. R. G. Greenler, A. J. Mallmann, J. R. Mueller, and R. Romito, Science 195, 360 (1977).
    [Crossref] [PubMed]
  11. R. G. Greenler, J. R. Mueller, W. Hahn, and A. J. Mallmann, Science (to be published).

1977 (1)

R. G. Greenler, A. J. Mallmann, J. R. Mueller, and R. Romito, Science 195, 360 (1977).
[Crossref] [PubMed]

1976 (1)

R. D. Edge, Am. J. Phys. 44, 780 (1976).
[Crossref]

1972 (3)

W. Evans and R. A. R. Tricker, Weather 27, 234 (1972);R. A. R. Tricker, Weather 25, 502 (1970);ibid. 28, 159 (1973);P. P. Hattinga Verschure, Weather 26, 532 (1971);ibid. 28, 300 (1973);R. E. Lacy, M. A. Ellison, and S. E. Ashmore, Weather 9, 206 (1954);G. W. Robertson, Weather 29, 113 (1974);R. Scutt, Weather 23, 525 (1968).
[Crossref]

R. A. R. Tricker, Q. J. R. Meteorol. Soc. 98, 542 (1972).

R. G. Greenler and A. J. Mallmann, Science 176, 128 (1972).
[Crossref] [PubMed]

1919 (1)

S. Fujiwhara and S. Oti, Bull. Cent. Met. Obs. Japan III, 33 (1919).

1794 (1)

T. Lowitz, Nova Acta Acad. Imp. Sc. Petropol 8, 384 (1794).(Although the account was published in 1794, the observation of the St. Petersburg complex was actually made on June 18, 1790, not July 1794 as reported in Refs. 5 and 7.)

Edge, R. D.

R. D. Edge, Am. J. Phys. 44, 780 (1976).
[Crossref]

Evans, W.

W. Evans and R. A. R. Tricker, Weather 27, 234 (1972);R. A. R. Tricker, Weather 25, 502 (1970);ibid. 28, 159 (1973);P. P. Hattinga Verschure, Weather 26, 532 (1971);ibid. 28, 300 (1973);R. E. Lacy, M. A. Ellison, and S. E. Ashmore, Weather 9, 206 (1954);G. W. Robertson, Weather 29, 113 (1974);R. Scutt, Weather 23, 525 (1968).
[Crossref]

Exner, F. M.

J. M. Pernter and F. M. Exner, Meteorologische Optik, 2nd ed. (Vienna and Leipzig, 1922).

Fujiwhara, S.

S. Fujiwhara and S. Oti, Bull. Cent. Met. Obs. Japan III, 33 (1919).

Greenler, R. G.

R. G. Greenler, A. J. Mallmann, J. R. Mueller, and R. Romito, Science 195, 360 (1977).
[Crossref] [PubMed]

R. G. Greenler and A. J. Mallmann, Science 176, 128 (1972).
[Crossref] [PubMed]

R. G. Greenler, J. R. Mueller, W. Hahn, and A. J. Mallmann, Science (to be published).

Hahn, W.

R. G. Greenler, J. R. Mueller, W. Hahn, and A. J. Mallmann, Science (to be published).

Humphreys, W. J.

W. J. Humphreys, Physics of the Air, (republication by Dover, 1964,Physics of the Air of the 3rd edition published by McGraw-Hill, New York, 1940).

Lowitz, T.

T. Lowitz, Nova Acta Acad. Imp. Sc. Petropol 8, 384 (1794).(Although the account was published in 1794, the observation of the St. Petersburg complex was actually made on June 18, 1790, not July 1794 as reported in Refs. 5 and 7.)

Mallmann, A. J.

R. G. Greenler, A. J. Mallmann, J. R. Mueller, and R. Romito, Science 195, 360 (1977).
[Crossref] [PubMed]

R. G. Greenler and A. J. Mallmann, Science 176, 128 (1972).
[Crossref] [PubMed]

R. G. Greenler, J. R. Mueller, W. Hahn, and A. J. Mallmann, Science (to be published).

Mueller, J. R.

R. G. Greenler, A. J. Mallmann, J. R. Mueller, and R. Romito, Science 195, 360 (1977).
[Crossref] [PubMed]

R. G. Greenler, J. R. Mueller, W. Hahn, and A. J. Mallmann, Science (to be published).

Oti, S.

S. Fujiwhara and S. Oti, Bull. Cent. Met. Obs. Japan III, 33 (1919).

Pernter, J. M.

J. M. Pernter and F. M. Exner, Meteorologische Optik, 2nd ed. (Vienna and Leipzig, 1922).

Romito, R.

R. G. Greenler, A. J. Mallmann, J. R. Mueller, and R. Romito, Science 195, 360 (1977).
[Crossref] [PubMed]

Tricker, R. A. R.

R. A. R. Tricker, Q. J. R. Meteorol. Soc. 98, 542 (1972).

W. Evans and R. A. R. Tricker, Weather 27, 234 (1972);R. A. R. Tricker, Weather 25, 502 (1970);ibid. 28, 159 (1973);P. P. Hattinga Verschure, Weather 26, 532 (1971);ibid. 28, 300 (1973);R. E. Lacy, M. A. Ellison, and S. E. Ashmore, Weather 9, 206 (1954);G. W. Robertson, Weather 29, 113 (1974);R. Scutt, Weather 23, 525 (1968).
[Crossref]

R. A. R. Tricker, Introduction to Meteorological Optics (American Elsevier, New York, 1970).

Am. J. Phys. (1)

R. D. Edge, Am. J. Phys. 44, 780 (1976).
[Crossref]

Bull. Cent. Met. Obs. Japan (1)

S. Fujiwhara and S. Oti, Bull. Cent. Met. Obs. Japan III, 33 (1919).

Nova Acta Acad. Imp. Sc. Petropol (1)

T. Lowitz, Nova Acta Acad. Imp. Sc. Petropol 8, 384 (1794).(Although the account was published in 1794, the observation of the St. Petersburg complex was actually made on June 18, 1790, not July 1794 as reported in Refs. 5 and 7.)

Q. J. R. Meteorol. Soc. (1)

R. A. R. Tricker, Q. J. R. Meteorol. Soc. 98, 542 (1972).

Science (2)

R. G. Greenler and A. J. Mallmann, Science 176, 128 (1972).
[Crossref] [PubMed]

R. G. Greenler, A. J. Mallmann, J. R. Mueller, and R. Romito, Science 195, 360 (1977).
[Crossref] [PubMed]

Weather (1)

W. Evans and R. A. R. Tricker, Weather 27, 234 (1972);R. A. R. Tricker, Weather 25, 502 (1970);ibid. 28, 159 (1973);P. P. Hattinga Verschure, Weather 26, 532 (1971);ibid. 28, 300 (1973);R. E. Lacy, M. A. Ellison, and S. E. Ashmore, Weather 9, 206 (1954);G. W. Robertson, Weather 29, 113 (1974);R. Scutt, Weather 23, 525 (1968).
[Crossref]

Other (4)

J. M. Pernter and F. M. Exner, Meteorologische Optik, 2nd ed. (Vienna and Leipzig, 1922).

W. J. Humphreys, Physics of the Air, (republication by Dover, 1964,Physics of the Air of the 3rd edition published by McGraw-Hill, New York, 1940).

R. G. Greenler, J. R. Mueller, W. Hahn, and A. J. Mallmann, Science (to be published).

R. A. R. Tricker, Introduction to Meteorological Optics (American Elsevier, New York, 1970).

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Figures (6)

FIG. 1
FIG. 1

Orientation of crystals that we consider. The major diagonal (AA′) of the basal face is constrained to lie in a horizontal plane but with arbitrary azimuth. The crystal may have any rotational orientation about the horizontal diagonal.

FIG. 2
FIG. 2

Three ray paths through the spinning crystal.

FIG. 3
FIG. 3

Lowitz arc simulations for a solar elevation of 30°. The letters correspond to the paths of the rays identified in Fig. 2. A circle of radius 22° and a line along the parhelic circle are included for reference.

FIG. 4
FIG. 4

Composite Lowitz arc simulations for nine solar elevations. Cross-hatched regions denote areas below the horizon.

FIG. 5
FIG. 5

Lowitz’s drawing of the St. Petersburg halo display of 1790.

FIG. 6
FIG. 6

Simulation of some of the arcs in Lowitz’s drawing for a sun elevation of 50°. Included are the 22° halo, circumscribed halo, Lowitz arcs, parhelic circle, 46° halo, infralateral arcs, and the part of the anthelic-arc extension that touches the 22° halo.