POLARIZATION OF SKYLIGHT 83 
larization (the plane of polarization horizontal) on the 
horizon and the positive polarization (the plane of 
polarization vertical) over the water surface around 
the observer. Similar phenomena over land were ob- 
served by Brewster as early as 1841. 
The biggest anomalies in the described distribution 
of polarization were observed after the volcanic erup- 
tions of 1883-1885, 1902-1903, and 1912-1914. The 
effect of the volcanic dust present in the atmosphere 
could be noticed in the extraordinarily low values of 
the degree of polarization. In 1884, Cornu [18] observed 
the rapid decrease of the maximum polarization from 
0.75 to less than 0.48; Dorno’s mean values for the 
zenith and h, = 0° were P = 0.557 for 1913 and P = 
0.739 for 1915. A very rapid increase of P during twi- 
light also appeared (Kimball [88]). Much larger effects 
could be observed in the positions of neutral points. 
1911 i912 
35° 
25° 
ANGULAR DISTANCE 
15° 
+3.5° = (O)s)9 ar Bose ~ 
SUN'S ELEVATION 
Fie. 3.—Distance of the Babinet point (Ba) from the sun 
and of the Arago print (A) from the antisolar point for different 
sun’s elevations h;. (Normal conditions—1911; after volcanic 
eruption of Katmai—1912). 
= [l3)9 
Besides the ordinary A- and Ba-points, Cornu [18] ob- 
served four neutral points symmetrically situated at 
the same elevation on both sides of the sun and the 
antisolar point. The distances of the A-point and Ba- 
point increased; the largest increase, however, was ob- 
served in 1902, and was more pronounced for the Ba- 
point, as was also observed to be true in 1912. In Fig. 3 
the mean values are compared for years with and with- 
out this effect; with respect to the A-point, the effect 
mentioned above, namely the increase of the distance, 
is clearly shown and the shift of minimum towards 
larger solar depressions also appears. The effect on the 
Ba-point curve is so great that its character is com- 
pletely changed; the curve is shifted to the other side 
of the A-point curve. 
Theory of Skylight Polarization 
The first correct step toward the explanation of sky- 
light polarization was made by Lord Rayleigh [50] in 
1871. He explained skylight polarization as the scatter- 
ing of sunlight on molecules and submicroscopic par- 
ticles with diameters much smaller than the wave 
length of the incident ray of light. If it is assumed that 
the scattering process takes place only once (primary 
scattering) and if refraction is neglected, the degree of 
polarization of partially polarized light in the direction 
¢ from the sun’s rays, 
P = (sin? g)/(1 + cos? ¢), (1) 
is a function of gy only. The maximum polarization oc- 
curs in the direction 90° from the sun, where the light 
is totally polarized (P = 1). There are two neutral 
points: one in the direction towards the sun, and one 
toward the antisolar pomt. Elsewhere the light is par- 
tially polarized with the plane of polarization defined 
by the sun, the observer, and the observed point in the 
sky. The theory agrees quite well with the observations 
with respect to the position of the point of maximum 
polarization and of the plane of polarization. But it 
does not explain the partial polarization at the point 
of maximum polarization and the existence of the ob- 
served neutral pomts. The assumptions of Rayleigh’s 
theory are apparently not satisfied exactly in the atmos- 
phere. The scattering particles are not isotropic and 
the theory should be modified for anisotropy of mole- 
cules (Cabannes [12]). The expression (1) then takes 
the form 
P = (1 — a) (sin? ¢)/(1 + cos? y+ asin? g) (2) 
in which a = 0.043 is the coefficient of depolarization. 
Thus the maximum polarization at ¢ = 90° is P= 
0.922, but the position of the neutral pomts is not 
affected by the anisotropy of molecules. 
The effect of secondary scattering, omitted in Ray- 
leigh’s theory, was studied as early as 1880 by Soret 
[64]. In the first approximation he considers only the 
light scattered by particles assumed uniformly dis- 
tributed in a ring around the horizon. In the center of 
the ring, with the sun at the horizon, the intensity of 
the light scattered by all particles in the ring has the 
components 
i, = 1b/4 =%,/8, ti, = 30b/4 = 31,/8, 
(3) 
1, = 2b, (b = const). 
Since the vertical component is predominant, the scat- 
tered light is negatively polarized in all directions along 
the horizon. In the direction 90° from the sun the com- 
ponent 7, is added to the primary scattered light, that 
is, the light is partially polarized. The neutral points 
are displaced to the positions where the positive polari- 
zation due to the primary scattering is compensated by 
the negative polarization of particles in the ring around 
the horizon. The distances of neutral points can be 
computed from relation (2) (cf. van de Hulst {68]). If 
P, and P denote the intensities of primary scattered 
light normal or parallel to the plane of polarization, 
and S, and S the intensities of secondary scattered 
light from the ring around the horizon, then a neutral 
