80 METEOROLOGICAL OPTICS 
Measurement of Skylight Polarization 
In the measurement of skylight polarization, there 
occur two different problems: measurement of the de- 
gree of polarization and measurement of the position 
of neutral points. 
The visual measurements of the degree of polariza- 
tion were highly developed by Cornu in his photopo- 
larimeter [17], and slightly improved by Martens [42]. 
This photopolarimeter contains a Wollaston prism as 
polarizer and a Nicol prism as analyzer. Both prisms 
can be rotated around the same axis and their mutual 
position and the position of the polarizer can be read off. 
With the analyzer fixed 45° to the principal axis of 
the Wollaston prism the plane of polarization is deter- 
mined by the position of the Wollaston prism in which 
both halves of the field in the eyepiece have the same 
intensity. The plane of polarization is then inclined 
45° from the principal axis of the Wollaston prism. If 
the Wollaston prism is now rotated by 45°, one half of 
the Wollaston prism transmits the intensity normal to 
the plane of polarization, the other the intensity in the 
plane of polarization. While the Wollaston prism is 
kept fixed the Nicol prism is rotated until both halves 
of the field have the same intensity. The degree of 
polarization P is then equal to cos 2, if w is the angle 
between the principal plane of the Wollaston and of 
the Nicol prism, usually readable by means of a scale 
outside of the instrument. 
The precision of this method was discussed by Smo- 
sarski [62] and found to be most accurate for large 
values of P; for small values of P this method requires 
some modification. Errors due to incorrect settings of 
the polarizer or of the analyzer can be eliminated by 
taking successive readings with the prism in the posi- 
tion 90°, 180°, and 270° from the original position. In 
this way a precision of 1-2 per cent can easily be 
reached, provided the illumination of the field m the 
eyepiece is sufficient to enable one to distinguish the 
unevenness of its halves. Another disadvantage is a 
relatively long time interval (about six minutes) nec- 
essary for all settings and readings. Because of the 
failure of this method in the case of rapid fluctuations 
in polarization or of inadequate illumination (during 
twilight or night), visual methods are being replaced 
more and more by objective methods. 
Because of the cumulative effect durmg longer ex- 
posures, photographic photometry is often used when 
the illumination is madequate. By means of a Wollaston 
prism a double picture of the measured field is obtained, 
and the degree of polarization is computed from the 
ratio of the intensities of the separate pictures. The 
precision of this method is limited by the precision m 
setting the principal section of the prism in or normal 
to the plane of polarization and in keeping it in this 
direction during the exposure. Especially during the 
night, when the illumination is very weak, this pro- 
cedure is very difficult. Another limitation of the photo- 
graphic method is the great variability of the pho- 
tographic material, which makes necessary a special 
sensitometric arrangement for the determination of a 
characteristic curve for each exposure. For exact meas- 
urement, a standard intensity scale must be simul- 
taneously exposed on the plate or film, and after de- 
velopment, the characteristic curve from the measured 
intensities is determined by a visual or photoelectric 
photometer. This procedure, unfortunately omitted by 
several authors, makes photographic polarization meas- 
urement rather complicated without any gain in pre- 
cision over the visual method (the accuracy seldom 
exceeds 5 or 10 per cent). However, if this procedure is 
not followed, the results are quite unreliable. On the 
other hand the photoelectric method seems to be more 
convenient for an objective polarization measurement. 
It offers not only the possibility of a fast and contin- 
uous measurement but also of measurement at low 
intensities. The continuous measurement can easily be 
made by measuring the intensity of light passing 
through a rotating Nicol prism or other analyzer [57]. 
If the prism rotates around its axis with a constant 
angular speed w, then the intensity of the photoelec- 
tric current from the photocell situated behind the 
prism is proportional to 147, + TI, cos? wt, if the time 
is counted from the moment when the principal plane 
of the prism (the plane of transmitted vibrations) is 
normal to the plane of polarization of the measured 
partially polarized light, the polarized and unpolarized 
components of which have intensities J, and J,, re- 
spectively. For light of greater intensity the current 
can be recorded continuously, and the degree of polar- 
ization determined from two intensities (maximum and 
minimum) if the period and the decrement of the galva- 
nometer or other recording system used is known. If 
the rotation of the prism is uniform and sufficiently 
slow, the direction of the polarization plane can also 
be determined by a very simple arrangement. By a 
suitable choice of the recording system even very rapid 
fluctuations in the polarization can be studied in this 
manner. The measurement of the polarization for low 
intensities can also be made without any basic diffi- 
culty if very sensitive photocells (photomultipliers) are 
used or if the photoelectric current is properly ampli- 
fied. Since a-c amplification is more effective, it is 
desirable to produce photoelectric alternating current, 
for which purpose fast rotation of the prism can con- 
veniently be used. 
Because the spectral sensitivity of the human eye 
differs from that of the photocell or the photographic 
material, the results of the objective methods will in 
general be different from that of the visual measure- 
ment. It can be shown [58] that, if there is no dispersion 
of the polarization, that is, if P is constant for all wave 
lengths, there will be no difference in the results of 
these different methods. But if the dispersion occurs, 
that is, P is different for different wave lengths, the 
difference between P measured by different methods 
will be greater, the greater the dispersion of the polari- 
zation. Since the dispersion depends upon the turbidity 
of the atmosphere, the difference between the results 
obtained by the different methods may vary appreci- 
ably from day to day. 
The measurement of the position of neutral points is 
