86 METEOROLOGICAL OPTICS 
study of the presence and the nature of larger scatter- 
ing particles. If the exact values of molecular scattermg 
are subtracted from the observed values, the remaiming 
part is the effect of larger particles, and it is quite evi- 
dent that, for such a purpose, observations should be 
used in which the deviation from the theory is most 
pronounced. This seems to be the case in the dispersion 
of skylight polarization. 
Dispersion of Atmospheric Polarization 
The discussion of polarization in the preceding sec- 
tion refers to “white” light, as it is observed directly 
by the human eye. The measurement of polarization 
in much shorter spectral ranges was started very early 
in skylight investigations. In 1884, Cornu [18] found 
the degree of polarization to be different for different 
colors. During this period of volcanic anomalies the 
polarization at shorter wave lengths was much larger 
than for longer wave lengths. The dispersion of polari- 
zation has been studied since that time by several au- 
ANGULAR DISTANCE 
SOLAR INTENSITY (CAL CM? MIN7') 
Fic. 4.—Distance of the Arago point from the antisolar 
point for h, = 10.5°, in different colors for different intensities 
of solar radiation (according to Neuberger). 
thors with one result confirmed by all, namely, the great 
variability of the dispersion with the turbidity, and 
thus with the weather, location, ete. Since the turbidity 
was not actually measured (except in the latest studies), 
the different results which have been attained are very 
difficult to compare. If the relativity of the terms 
“ure” and “turbid” atmosphere is admitted, then the 
contradictory results of different authors, even recently 
considered inexplicable [8], can be ordered to show a 
definite trend, confirmed by theoretical considerations. 
For very low turbidity (high altitude) the degree of 
polarization at the point of maximum polarization in- 
creases with the wave length [65]. With increasing tur- 
bidity, the maximum is shifted to the central part of 
the visible spectrum and the difference between polari- 
zation in the red part of the spectrum (P,) and m the 
blue part (P;) is decreased (for “pure air” in Gockel’s 
definition the difference P, — P, becomes smaller than 
the errors of observation). With still larger turbidity 
the maximum is shifted to the blue part, that is, 
P, > P, (22, 25, 34, 48, 65].- 
The measurement of distances of neutral points in 
different colors was started by Jensen [1] in 1909. The 
results of his measurements were confirmed by Busch 
[11], who found that the distances of the A-point were 
larger the shorter the wave lengths. During the abnor- 
mal period 1912-14, just the opposite was found. This 
result was recently confirmed by Neuberger [45, 46] in 
his measurement of the A-point at h, = 10.5°. Along 
with the A-point distances, the intensity of solar radi- 
ation, the blue color of the sky, etc., were measured 
and the variations of A-point distances with the tur- 
bidity were proved to be as shown in Fig. 4. 
The dispersion of polarization is thus very sensitive 
to the degree of turbidity and could be used as another 
indicator of turbidity. But it can also be used for 
answering the question about the prevailing effect of 
the molecular scatterimg, or of the presence of larger 
particles in the atmosphere. It is evident that in Ray- 
leigh’s theory of primary scattering there is no disper- 
sion, since the degree of polarization P is independent 
of X. If it is assumed with Milch that the light scat- 
tered by large particles is unpolarized, the component 
of the total intensity due to the scattering on large par- 
ticles can be expressed in the form F, = d—% Nf(¢), 
where a decreases from 3.5 to 1 with increasing size of 
particles, N denotes the number of such particles per 
unit volume, and ¢ is the scattering angle. It can easily 
be shown [59] that the sign of the difference P(A) — 
P(Xo) is determined by the sign of the expression 
[p/PQo) — I— x4) + Gt = x) Fa(A0)/To(ro), (8) 
where p denotes the degree of polarization in Rayleigh’s 
theory of primary scattermg, given in equation (1), 
x = Xo/X, and J, is the total intensity of the component, 
due to the primary scattering. If the turbidity is small, 
F,—0 and P(X) > P(X\o) whenever \ > Xo. With in- 
creasing turbidity (F, > 0), the second term in (8), 
having an opposite sign from the first one, reduces the 
difference P(A) — P(\o) and for a sufficiently large 
turbidity reverses the sign of P(X) — P(Ao). The vari- 
ation of the dispersion with increasing turbidity can 
thus be explained in agreement with observation. But 
the discussion of the distance of the neutral points for 
different wave lengths shows clearly that the assump- 
tion made by Milch, that the light scattered by large 
particles is unpolarized, is not justified. If the light 
scattered by large particles is assumed to be unpolar- 
ized, the distance of neutral poimts is given by equa- 
tion (4) written in the form 
P4(Ao) sin? ho = S(Ao, ho) — Si(Ao, ho), 
and for \ # Xo, 
Px(Xo) sin? h = x* [S(Xc, h) — Si(Ao, h)]- 
Since S; is actually independent of h, S can be ex- 
pressed by S; and the ratio Si(X\o)/Pi(o) can be elim- 
inated from these two equations. The resulting equa- 
tion can be written in the form 
sin? h — sin? ho 
5 — 7sin? ho 
eee eee co) 
(6 1) sin? ho Gana (9) 
