POLARIZATION OF SKYLIGHT 87 
Since hy) < 30°, the numerator and the denominator in 
(9) are always positive, and h > ho whenever Xo > X. 
The distances in blue are larger than in the red part of 
the spectrum, in agreement with the observation made 
for very low turbidity. However, the computed differ- 
ence h — hy, for a given ho and given wave lengths 
X, Xo, is about twice as large as observed. What is more 
serious, the great variability of this difference with in- 
creasing turbidity cannot be explained by (9). The ef- 
fect of increasing turbidity can be taken into consid- 
eration only by increasing ho, but the right-hand side 
of (9) increases with hy instead of the observed decrease 
to negative values. This may serve as a proof of the 
incorrectness of the assumption made above. For a com- 
plete discussion it is necessary to include the polarized 
component due to the scattering by large particles also. 
This can be done only by using the Mie-Debye theory, 
as discussed in detail elsewhere [59]. By constructing a 
special model of the distribution, size, and optical prop- 
erties (refractive index) of the large particles, the dis- 
persion of polarization can be computed and compared 
with the observed values through a procedure similar 
to that used in the study of atmospheric haze [28, 51, 
60] and thus a model of the distribution which best fits 
the observations can be found. 
Polarization Anomalies During Twilight 
The same information concerning the size, nature, 
and distribution of scattering particles in the atmos- 
phere can be obtained from any deviations of observed 
values of skylight polarization from those to be ex- 
pected from Rayleigh’s theory. Particular emphasis has 
been placed on anomalies during twilight (because of 
the easily determined changes in illumination along the 
vertical line to the zenith) with the hope that more in- 
formation can be obtained about the vertical distribu- 
tion of scattering particles in this way. But the use of 
twilight anomalies is not as simple as it would seem. 
The first difficulty is the rapid decrease of the intensity 
of skylight, which causes serious difficulties in polari- 
zation measurement. Visual methods quickly become 
uncertain and are very seldom reliable for solar depres- 
sions beyond h, = —5° or —6°. The photographic 
method requires longer exposures during which the 
eventual fluctuations in the degree of polarization and 
in the position of the plane of polarization may cause 
large systematic errors. 
In theoretical investigations the atmosphere can no 
longer be considered as plane-parallel, and refraction 
must be taken into consideration at least to the extent 
of estimating the limit of the earth’s shadow. The 
ground reflection, acting for low solar depressions only 
on one side of the horizon, and the different extinction 
values in the solar and antisolar regions make the com- 
putation of the sky polarization rather complicated. 
With respect to the effect of secondary scattering, it is 
valid to offer the same criticism which was presented 
against the use of the zenith intensity for optical sound- 
ing of the upper atmosphere. As Hulburt [27] pointed 
out, the intensity of the secondary scattering increases 
rapidly in comparison with the intensity of primary 
scattering, so that for solar depressions larger than 8°, 
the secondary scattering from the lower level has a 
greater intensity than that of the primary scattering 
from the upper levels still illuminated by direct rays 
from the sun. Hulburt’s estimate of this effect was 
based on the measured intensity of skylight near the 
western horizon; the presence of larger particles was 
thus taken into consideration. This may explain the 
much larger values for the ratio of the intensity of the 
secondary and primary scattering (Iprim: Isee = 1:185, 
h; = —10°9’) than computed by Link [39] (lorm: 
Tsec = 2:1) under the assumption of molecular scat- 
tering only. For this reason it is quite difficult to ex- 
plain the high correlation of the polarization anomalies 
(sudden or nonmonotonic decrease of P in the zenith 
for sun’s depressions larger than 10°) with the changes 
in the ionization of the H- or F-layer, as observed by 
Khvostikov and a group of Russian scientists. The first 
attempt to explain the anomalies as being associated 
directly with the increase of anisotropy of the ions as 
compared to neutral particles [35, 36, 52] was found by 
Ginsburg [23, 24] to be unacceptable because of the 
predominant effect of the secondary scattering. The 
polarization caused only by secondary scattering under 
such conditions was recently estimated by Rosenberg 
[53] as being even larger than observed. The observed 
rotation [49] of the plane of polarization from the direc- 
tion given by the position of the sun cannot be ex- 
plained simply by the asymmetry in the solar illumina~ 
tion and should be studied more closely in relation to 
the problem of fluorescent luminescence or other types 
of emission of the night sky. For the study of the emis- 
sion layer the scattering of the emitted hght is very 
important and can be used for the determination of the 
height of the emission layer [8]. Since the secondary 
scattered solar radiation may be superimposed upon 
the light from the emission layer, the dispersion of 
polarization of the twilight or night sky could be used 
for separating the phenomena of the lower atmosphere 
from those of the upper levels. Because of experimental 
difficulties there is little hope for the effectiveness of 
this method in the near future. The only possible way 
of separating the intensity of the polarization produced 
in lower levels from the phenomena related to upper 
levels is to compute these quantities using the extine- 
tion coefficient and other parameters of scattering im 
lower levels, obtained by independent measurements. 
For this purpose the method of an artificial light source 
seems to be quite adaptable. The searchlight beam has 
been used and information about the type and the law 
of scattering has been derived mainly from the total 
intensity measurement [28, 29, 33, 51, 60]. More infor- 
mation can be obtained, however, if the measurement 
of the polarization is added, as has been done by 
Khvostikov [35]. But since the brightness of the search- 
light beam decreases with the distance from the source, 
the secondary scattering in lower levels should be care- 
fully taken into consideration before any conclusions 
are made about scattering in higher levels. 
The searchlight-beam method definitely offers quite 
new possibilities and if properly used may contribute 
