82 METEOROLOGICAL OPTICS 
a sun’s elevation between —2° and —4°. The increase 
of polarization for h, < 0 was found to be more rapid, 
the lower the value of the polarization at h, = 0. 
The distribution of the polarization over the sky was 
studied extensively by Dorno [22]. In a stereographic 
projection with the sun at its pole, the lines of equal 
polarization are nearly concentric circles around the 
sun. For corresponding P, the circles on the sun’s side 
are closer to the equator (the line of maximum polari- 
zation) than on the antisolar side, showing a slight 
asymmetry of P in the sun’s vertical, a fact studied 
and proved by Smosarski [62]. The distribution—sur- 
prisingly—varies very little with the elevation of the 
sun above the horizon. 
The position of the plane of polarization was also 
measured and, at first, lines were drawn parallel to the 
direction of this plane. Later on they were replaced by 
the lines connecting points with the same inclination of 
the plane of polarization to the vertical (polarization 
isoclines). Since the inclination 45° to the vertical, 
called also a neutral line or Busch lemniscate, can 
easily be measured by the interruption of the vertical 
fringes in a polariscope (similar to the neutral points), 
it was studied extensively by Dorno [22] and Mentzel. 
Mentzel’s measurements were recently revised by Dalh- 
fore suggested by Jensen [80] as reliable indicators of 
atmospheric turbidity. Comparing the mean values for 
winter and summer from a period with a fairly normal 
condition, Jensen concluded that, with increasing tur- 
bidity, (1) the antisolar distances of the A-point in- 
crease, (2) the difference between the maximum and 
the secondary minimum for the A-point increases, and 
(8) the position of the minimum in the A-point curve 
is shifted to the negative h,. The variations in the dis- 
tances of the Ba-poit do not follow such simple rules, 
being more sensitive to the conditions at much higher 
levels which are unaffected by the seasonal variations. 
Neuberger [45] studied the interrelationship between 
the extremes in the A-point curve and found a very 
high correlation (+0.95 + 0.01) between the difference 
in (2) and the distance of the A-point for h, = 10.5° 
or 13.5°, suggesting that a single measurement of the 
A-point distance for these values of h, can be used as 
an indicator of the turbidity. When he compared the 
distance of the A-point at h, = 10.5° with the direct 
measurement of solar radiation, Neuberger found an 
increase of this distance with decreasing intensity of 
solar radiation; this would agree with the statement in 
(1) above. 
As another indicator of turbidity, the difference be- 
TasiE I. DirreRENCE BETWEEN A-POINT AND Ba-porntT Distances (in degrees) 
fis = SS he 452 jis = OP hs = 2.5° hs = 1.5° hs = 0.5° hs = —0.5° 
Efambunes 1 909 S1eeer eee ere 5.9 5.0 4.1 3.3 2.3 1.4 0.9 
Arnsberg, 19091 sen oes eee 6.3 5.6 4.6 3.8 2.9 2.1 1.6 
IDENHOS, WA UM. Coen osvessscc00 0.1 0.3 0.5 0.5 0.1 —0.1 —0.2 
IDENOS, Homme MM... o55o000ccs0es05 0.9 0.0 1.0 0.6 0.1 = — 
kamp and Kantus [20] and discussed with respect to 
the possibility of usmg the shape or the area inside the 
Busch lemniscate as a measure of the turbidity. 
More attention has been devoted to the measurement 
of the position of neutral points than to the measure- 
ment of the degree of polarization. The reason for this, 
besides the great simplicity of the measurement, is the 
great variability of these positions, and their greater 
sensitivity to the turbidity of the atmosphere. The 
measurements mostly relate to the Arago and Babinet 
points; the position of the Brewster point has not been 
studied systematically because it is difficult to measure 
(below the sun, close to the horizon). The distance of 
the Arago point from the antisolar point and of the 
Babinet point from the sun vary in a characteristic 
way for small positive and negative elevations of the 
sun. If the distances of these points (A- and Ba-points) 
are plotted against the sun’s elevations, then the curve 
for the A-point shows a minimum (or a secondary mini- 
mum) for small negative h,, while—under normal con- 
ditions—the Ba-poit curve shows a secondary maxi- 
mum (cf. Fig. 3). These extremes in both curves are 
followed by a rapid increase for larger negative h,. The 
position and the values of those extremes (for the Ba- 
point, even the whole character of the curve) change 
greatly with the turbidity; these quantities were there- 
tween the points of the A- and Ba-point curves for the 
same i, can be used. This difference increases with in- 
creasing turbidity, as is clearly shown in Table I, where 
the values of this difference, measured in a turbid at- 
mosphere (Hamburg, Arnsberg), are compared with 
those measured in a much less turbid atmosphere 
(Davos). 
Quite distinct is the effect of ground reflection on the 
curve of A-point distances. The maximum, which at a 
land station is usually very flat and is observed around 
h, = 12.5°, shifts to smaller sun’s elevations and de- 
creases in value in the vicinity of large water surfaces 
[80]. If the reflection is strong, new neutral points ap- 
pear, either below the ordinary points (as observed by 
Rubenson [54] below the Ba-point, and by Jensen [8] 
and Neuberger [44] below the A-point) or on both sides 
of the sun at the same elevation (Soret [63]). In a 
polariscope the fringes are visible even over the water 
surface, in the sun’s vertical, with a dark central band 
(positive); in other directions they show a bright cen- 
tral band (negative). In a position closer and closer to 
the observer as the direction approaches 90° from the 
sun’s vertical, the negative fringes change rapidly into 
the positive, suggesting the existence of a series of neu- 
tral points, or better, the existence of a transition zone 
(Umkehrzone, Jensen [8, 30]) between the negative po- 
