OF ELLIPTIC POLARIZATION. 
307 
merits of these two angles of incidence will be equal radii of the ellipse, and 
consequently the azimuth which bisects the two azimuths in question, will be 
that of the major axis of the ellipse. By increasing the angle of incidence on 
the second plate, other two azimuths containing equal radii of the ellipse will 
in like manner be found ; and we might, if necessary, at last obtain an angle of 
incidence where the two radii coincided with the greater axis. 
The position of the ellipse being thus given, we may determine it for all 
angles of incidence. Calling x the angle of incidence on the first plate, then 
we shall have four points in the ellipse as follows. The radii in azim. 90° and 
2/0° are always 90° — x, and the radius in azim. 0° and 180° is the comple- 
ment of the angle of incidence at which <p in the last equation has the same 
value as at the angle x. Hence the form of the ellipse is also given. 
In these experiments the polarization of the primitive ray has always been 
+45°. When this plane varies its position, that of the restored ray also 
changes, as we have already shown ; but it remains to be seen what change 
takes place in the angles of restoration. At all angles of incidence, a variation 
in the plane of primitive polarization does not alter the angles of restoration 
or the corresponding radii of the ellipse in azim. 0°, 90°, 180°, and 270° ; but at 
all intermediate azimuths of the second plate the angles of restoration diminish 
while the primitive plane varies from 45° to 0°, and increase when it varies 
from 45° to 90°. The following experiments show the progress of the change 
when the azimuths of the second reflexion are +45° and —45°. 
Steel. 
Inclination of Plane of Azimuth of Second Reflexion Azimuth of Second Reflexion 
prim. Polarization. 
-(-45° 
Observed. 
to Right. 
Calculated. 
Observed. 
45° to Left. 
Calculated. 
O 
o 
o 
/ 
O 
O / 
0 . . 
. o : 
0 
0 . 
. . 1 
0 0 
5 . . 
2 
2 
4 . 
. . 2 
10 
10 . . 
4 
3 
46 . 
• • 3* 
2 3 
15 . . 
. 6 
5 
43 . 
• • 41 
..37 
20 . . 
GO 
7 
50 . 
. . 6 
. . 4 14 
25 . . 
.11 
9 
54 . 
. . 6 
5 26 
30 . . 
. 13 
12 
11 . 
• • 7 
6 43 
35 . . 
. 15 
14 
40 . 
. . 8 
8 6 
40 . . 
. 18 . 
17 
25 . 
• - 91 
9 41 
45 . . 
• 20i . 
20 
o 
co 
. . Ill 
. . 11 30 
