72 METEOROLOGICAL OPTICS 
instead of the sine of the whole angle 6. This is also true 
for the anticorona [6, equation (48)], the theory of which 
shows that it is produced by rearward diffraction, not 
by reflection of the primary ray with subsequent for- 
ward diffraction [Richarz, ec. 42]. Bucerius’ results may 
be summarized as follows: The intensity of the corona 
is x? = (ad/d)? times as great as that of the anticorona; 
the intensity at the center of the anticorona is a mini- 
mum, that of the corona a maximum. Values for the 
angle @ of the successive intensity maxima of the anti- 
corona’ are determined by 2a sin (0/2) = 3.05, 6.7, 
10.0, 13.2, --- ; the minima are located at relatively 
the same position as are the corona maxima (Table 
VIII). This explains why the application of the classical 
corona formula (6) to the minima of the anticorona 
yielded values of the drop diameter d, that varied with 
the order of the minimum [e. 42, 47]. Also the decrease 
in intensity of successive maxima is much greater for 
the corona than for the anticorona; therefore, multiple 
glories are more frequently observable than multiple 
coronas. 
The old controversy regarding the possibility of cor- 
onas and glories in ice-erystal clouds [21] now stands as 
Unfortunately, none of the new theories considers dif- 
fraction by nonspherical particles, so that no final 
decision can be made. 
Iridescence of clouds is explained as diffraction pat- 
terns produced by groups of uniform droplets that vary 
in size in different portions of the cloud. In view of the 
great sensitivity of the diffraction patterns to slight 
differences in size of small droplets [45] (Fig. 10), it is no 
longer difficult to explam the occurrence of iridescence 
at relatively large angular distances from the sun [c. 42]. 
The heiligenschein is considered the result of external 
reflection by the dew droplets [21, 42]; to what extent 
diffraction plays a role in this phenomenon is not 
known. Experimental data or imtensity measurements 
are completely lacking. 
The corona and anticorona have been widely em- 
ployed in the study of cloud and fog elements. Measure- 
ments were largely confined to the angular radius of 
prominent rings and subsequent evaluation in terms of 
droplet radius. In view of recent theoretical develop- 
ments [6, 20, 45] this geometric method seems unre- 
liable; also the difficulty im visually locating diffuse 
rings, produced by inhomogeneous fogs or clouds, causes 
Tasie VIII. Comparison or Position or Corona Maxima or VARIOUS ORDERS ACCORDING TO DIrFERENT THEORIES 
Order of Maximum 
Author Argument of Bessel Function 
1 2 3 4 i 5 
Mascart [c. 21] d(sin 6)/2 5.14 8.46 11.67 14.84 17.98 
Ramachandran [45] # 5.14 8.42 11.62 14.78 17.96 
Breasts [4 Qn d(sin 6/2)/r Hi 8.4 | LG 14.8 fi, 
follows: Multiple-colored rings generally indicate the 
presence of water droplets; however, the production of 
faintly colored glories by ice clouds has been established 
[47]. A statistical survey by Peppler [41] revealed that 
78 per cent of glories were simultaneously observed with 
fogbows at temperatures between OC and —4C; a 
maximum frequency of glories occurs at about —4C, 
that of halos at about —12C. Nevertheless, the fre- 
quency curves of anticoronas and halos overlap i a 
wide range of temperatures from about —2C to < 
—20C. At any rate, this problem cannot be considered 
solved. Statistical analyses of the occurrence of diffrac- 
tion rings simultaneously with halos or fogbows reveal, 
at best, the relative frequency of diffraction rings in ice 
and water clouds, respectively, but are entirely incon- 
clusive regarding the physical possibility of these phe- 
nomena in ice clouds. Moreover, Stranz [c. 36] by means 
of photronic cells, detected multiple coronas that were 
invisible to the eye. The theoretical objections to the 
possibility of diffraction phenomena produced by ice 
clouds were mainly based on the optical properties and 
orientation of ice needles, but other possible crystal 
forms must also be considered. Moreover, the occurrence 
of Bishop’s ring in dust clouds shows that nonspherical 
particles are capable of producing diffraction rings. 
7. Bucerius (also [36]) gives here 272 sin (6/2), but refers 
to it as the argument of the Bessel function which, however, 
appears as 2rd(sin 0/2)/X = 2x sin (6/2). 
considerable uncertainties (see [5]). In the future it 
would be preferable to resort to objective monochro- 
matic photometry of the entire zone around the light 
source (or shadow center), and perhaps, to determine 
the intensity of the diffracted light separately for the. 
two components of polarization. Simultaneous deter- 
mination of the droplet size by other means could serve 
as a check of the theory by making possible a compari- 
son between observed and theoretical intensity dis- 
tributions, rather than a comparison of only the mmima 
or maxima. 
Considering the rarity of homogeneous fogs, a theo- 
retical and experimental study of inhomogeneous fogs 
appears of particular practical importance. Also, a final 
answer to the question of the possibility of coronas mm 
ice clouds would give the observer on the ground a tool 
for the identification of the physical state of the clouds. 
TWILIGHT PHENOMENA 
The investigation of twilight phenomena is closely 
connected with the study of the optical properties of 
the upper atmosphere, at least to a height of 60 km 
[18] and, thus, indirectly with the study of its density 
and dust content. The discussion of the temporal de- 
velopments of the various phenomena is based on the 
sunset and the sun’s meridian. Figure 11 shows the 
nomenclature for the significant astronomic-geometric 
features pertaining to the half-space above the observer 
and a schematic view of the major phenomena. 
