Abstract

A display of halos of unusual radii occurred on 14 April 1974, and was visible in southern England and in Holland. Photographs of the display were taken by Professor Scorer and the present author was privileged to examine them. They showed not only circular halos but also arcs tangential to some of them. The investigation described in the following paper was undertaken to try to elucidate the mechanisms by which these arcs might be formed. It led to a new theory of the formation of circular halos and also of the tangential or quasitangential arcs associated with them. It also led to a picture of the shape of the ice crystals giving rise to this particular display.

© 1979 Optical Society of America

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References

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  1. W. J. Humphreys, Physics of the Air (McGraw-Hill, New York, 1929), pp. 534–536.
  2. Louis Besson, “Concerning Halos of Unusual Radii,” Mon. Weather Rev., May, 254–255 (1923).
    [CrossRef]
  3. R. A. R. Tricker, Introduction to Meteorological Optics (American-EIsevier, New York, 1970), pp. 76–78.
  4. E. C. W. Goldie, G. T. Meaden, and R. White, “The concentric halo display of 14th April 1974,” Weather 31, No.  9, 304–312 (1976).
    [CrossRef]

1976 (1)

E. C. W. Goldie, G. T. Meaden, and R. White, “The concentric halo display of 14th April 1974,” Weather 31, No.  9, 304–312 (1976).
[CrossRef]

1923 (1)

Louis Besson, “Concerning Halos of Unusual Radii,” Mon. Weather Rev., May, 254–255 (1923).
[CrossRef]

Besson, Louis

Louis Besson, “Concerning Halos of Unusual Radii,” Mon. Weather Rev., May, 254–255 (1923).
[CrossRef]

Goldie, E. C. W.

E. C. W. Goldie, G. T. Meaden, and R. White, “The concentric halo display of 14th April 1974,” Weather 31, No.  9, 304–312 (1976).
[CrossRef]

Humphreys, W. J.

W. J. Humphreys, Physics of the Air (McGraw-Hill, New York, 1929), pp. 534–536.

Meaden, G. T.

E. C. W. Goldie, G. T. Meaden, and R. White, “The concentric halo display of 14th April 1974,” Weather 31, No.  9, 304–312 (1976).
[CrossRef]

Tricker, R. A. R.

R. A. R. Tricker, Introduction to Meteorological Optics (American-EIsevier, New York, 1970), pp. 76–78.

White, R.

E. C. W. Goldie, G. T. Meaden, and R. White, “The concentric halo display of 14th April 1974,” Weather 31, No.  9, 304–312 (1976).
[CrossRef]

Mon. Weather Rev., May (1)

Louis Besson, “Concerning Halos of Unusual Radii,” Mon. Weather Rev., May, 254–255 (1923).
[CrossRef]

Weather 31 (1)

E. C. W. Goldie, G. T. Meaden, and R. White, “The concentric halo display of 14th April 1974,” Weather 31, No.  9, 304–312 (1976).
[CrossRef]

Other (2)

W. J. Humphreys, Physics of the Air (McGraw-Hill, New York, 1929), pp. 534–536.

R. A. R. Tricker, Introduction to Meteorological Optics (American-EIsevier, New York, 1970), pp. 76–78.

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Figures (15)

FIG. 1
FIG. 1

Humphrey’s nomenclature for crystal faces.

FIG. 2
FIG. 2

Bragg’s unit cell for ice crystals.

FIG. 3
FIG. 3

Position of normals in doubly oriented crystals with their principal axes horizontal.

FIG. 4
FIG. 4

Location of the pole of the normal plane.

FIG. 5
FIG. 5

Refraction in the normal plane.

FIG. 6
FIG. 6

Arcs associated with halos of unusual radii, arising from crystals that have their principal axes and one prismatic face horizontal. Solar elevation 0°. These arcs are not arcs of contact except at certain solar elevations.

FIG. 7
FIG. 7

Same arcs as in Fig. 6 for a solar elevation at 10°.

FIG. 8
FIG. 8

Arcs of contact to halos of unusual radii arising from crystals having their principal axes horizontal. Solar elevation 0°. (Arcs wholly below horizon omitted.)

FIG. 9
FIG. 9

Same arcs as in Fig. 8 for a solar elevation of 10°.

FIG. 10
FIG. 10

Position of normals in crystals having their principal axes vertical.

FIG. 11
FIG. 11

Arcs associated with halos of unusual radii arising from crystals having their principal axes vertical. These arcs are not arcs of contact except at certain solar elevations. ∑ = 0°.

FIG. 12
FIG. 12

Same arcs as in Fig. 11 for a solar elevation of 10°.

FIG. 13
FIG. 13

E. C. W. Goldie’s measurements of Scorer’s photographs of the display of Easter, 1974.

FIG. 14
FIG. 14

Crystal with truncated pyramidal faces.

PLATE 100
PLATE 100

(R.A.R. Tricker, p. 1093). One of Professor Scorer’s photographs of the display of Easter, 1974.

Tables (1)

Tables Icon

TABLE I Comparison of results with Besson’s values

Equations (15)

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

μ = μ ( 1 cos 2 θ / μ 2 ) 1 / 2 sin θ
cos N 1 N 2 = sin μ 1 sin μ 2 + cos μ 1 cos μ 2 cos ( λ 2 λ 1 ) .
A = 180 ° N 1 N 2 .
cos Z N 1 N 2 = sin μ 2 sin μ 1 cos N 1 N 2 cos μ 1 sin N 1 N 2 ,
cos P = cos μ 1 sin Z N 1 N 2 .
cos L = sin μ 1 cos P cos μ 1 sin P ,
B = R Q = λ 1 L .
cos ν = sin μ 1 / sin P .
cos θ = sin cos P + cos sin P cos ( B β ) .
cos δ = sin cos θ cos P sin θ sin P .
i 1 = ν + δ .
sin μ ¯ = cos θ cos P + sin θ sin P cos ( δ D ) .
cos S Z K = cos θ sin μ ¯ cos P cos μ ¯ sin P ,
λ = B β S Z K .
p 1 p 1