GENERAL METEOROLOGICAL OPTICS 69 
could be made, for example, with the aid of a spatial 
arrangement of a field of light sources and receivers in 
connection with a dense micrometeorological network. 
For recording the apparent vibration of objects, motion 
picture cameras could be employed, whereas photo- 
electric devices seem to be preferable for measuring the 
apparent intensity fluctuations. The variation of scintil- 
lation with the altitude of the ray path above the 
eround, as well as with oblique upward and downward 
direction of the rays, is another problem which seems 
of practical interest for flight operations. 
PHENOMENA DUE TO ATMOSPHERIC 
SUSPENSIONS 
Tn this section, the sun is considered as the source of 
light, although the moon or artificial luminants may 
also produce the phenomena. 
Halos. The term “halo,” although implying ring 
shape, is generally applied to all optical phenomena 
that are produced by ice crystals suspended in the 
atmosphere and, occasionally, by those deposited on 
the ground [34, 36]. 
In Fig. 9, the sun is roughly 25° above the horizon 
HH; ring A represents the 22°-halo (radius 22°), ring B 
the 46°-halo. The two parhelia CC lie to the right and 
left of the sun at the same elevation, but at angular 
distances from the sun that vary between 22° and 32° 
for sun’s elevations between 0° and 50°, respectively. 
The parhelic circle DD through the sun and parallel to 
the horizon is rarely seen as a complete ring; often only 
short segments of it extend outward from the parhelia. 
Tangent to the 22°-halo are the wpper and lower tangent 
arcs HE and H’E’, respectively, which are only one of 
the metamorphic forms of the circwmscribed halo. This 
halo is truly circumscribed only for sun’s elevation of 
> 30°. For the various forms of this halo see pertinent 
literature [21, 34, 42]. The lateral tangent arcs of the 
22°-halo, or Lowitz-arcs, FF, curve concayely toward 
the sun from the parhelia and touch the 22°-halo below 
its equator. The vertex (in the sun’s meridian) of the 
Parry-arc G has an angular distance from the sun that 
decreases from 43° at O° sun’s elevation to tangency 
with the 22°-halo for sun’s elevations between 40° and 
60°, and then increases again for higher sun’s elevations. 
The circumzenithal arc J is centered around the zenith 
and very near, or even tangent to, the 46°-halo. The 
infralateral tangent arcs of the 46°-halo are represented 
by AK; these arcs also are metamorphosed as their 
points of tangeney move downward and meet at a sun’s 
elevation of 68°, while at the same time their curvature 
(convex toward the sun) decreases and reverses itself 
for sun’s elevations > 58°. The single are separates from 
the 46°-halo when the sun is higher than 68°. The 
sun pillar LL lies in the sun’s meridian and is, like the 
parhelic circle, generally white because of its origin 
by reflection, whereas the other halos are produced by 
refraction and thus more or less colored. 
There are also other halos, such as the czrcwmhori- 
zontal arc that corresponds to the circumzenithal arc, 
but lies about 46° below the sun. Swpralateral tangent 
arcs of the 46°-halo correspond to the infralateral arcs. 
On the sky opposite the sun, the anthelion, a bright spot 
on the parhelic circle, is sometimes obliquely crossed by 
anthelic arcs. Also rings of unusual radu, 8—9°, 17-19°, 
23-24°, etc., have been observed on rare occasions, as 
well as skewed forms such as inclined pillars and par- 
helic circles, and secondary phenomena caused by reflec- 
tion or refraction of light emitted from primary halos. 
The geometrical optics of the various halo phenomena 
was theoretically treated by various authors [21, 34, 
42, 44, 58]. In general, most phenomena can be ex- 
plained by refraction with minimum deflection and/or 
by reflection involving simple hexagonal ice crystals of 
columnar or platelet shape, with various attitudes and, 
in some cases, oscillating motion while falling. The 
principal genetic features of the major halo phenomena 
are summarized in Table VII, in which the optical 
relationship, for example, between the circumzenithal 
are and the infralateral ares of the 46°-halo, becomes 
evident. There are, however, many phenomena that 
have been explained by different patterns of ray paths, 
or by more complicated crystals or crystal aggregates. 
Thus, for example, the optical origin of the anthelion, 
its oblique ares [53], Hevelius’ parhelia at about 90° 
Fre. 9.—Schematic view of major halo phenomena. 
from the sun, and other phenomena, is still uncertain; 
Bouguer’s halo, a white ring of about 38° radius around 
the anthelic point, may even be a fogbow produced by 
very small supercooled water droplets [84, 47]. Decisive 
explanations will not come from additional theories, 
but from an accumulation of better observations. In 
particular, sampling of the ice crystals producing rare 
halos or those of uncertain origin would be most desir- 
able. Many halos, theoretically established, have never 
been observed [58]; on the other hand, some phenomena, 
such as those observed by Arctowski [e. 42], are still 
unexplained. Meyer [34] discusses the various geometric 
problems of halo phenomena, and outlines as prerequi- 
sites for a complete theory the various physical aspects, 
such as the concentration of ice crystals in the clouds, 
and the brightness and polarization of the halos relative 
to those of the clouds in the environment. The physical 
optics of halos is almost entirely unexplored; in addition 
to refraction and/or reflection by ice crystals, diffrac- 
tion plays a role in the formation of halos [84, 42]. 
Photometric observations, that have been introduced 
into halo investigations by E. and D. Briiche [5], would 
advance our pertinent knowledge of halos and the 
constitution of ice clouds [84]. 
