OF ELLIPTIC POLARIZATION. 
303 
reflexion into azim. 45° or 225°, we shall find that the angle of restoration is 
no longer 75°, but 78°. At azim. 90° and 2/0° it is again 75°, and in azim. 135° 
and 315° it is only 68°, having varied from 68° to 78°. 
The following Table shows the observed and calculated angles of restoration 
in different azimuths. 
Complement of Angles of Restoration, 
Azimuths from Plane of first Angles of Restoration or Elliptical Radii. 
Reflexion. from Steel. Observed. Calculated. 
o o o o o 
0 
and 180 . 
... 75 . 
. . . 15 . . 
. 14.9 
22i 
. 2021 . 
... 77 • 
. . . 13 . . 
. 12.7 
45 
. 225 . 
... 78 . 
. . . 12 . . 
. 12 
6 7\ 
. 24 7\ • 
... 77f . 
... 121 . . 
. 12.7 
90 
. 270 . 
... 75 . 
. . . 15 . . 
. 14.9 
112i 
. 2921 . 
... 70 . 
. . . 20 . . 
. 19 
135 
. 315 . 
... 68 . 
. . . 22 . . 
. 22 
157* 
• 337^ • 
... 70 . 
. . . 20 . . 
. 19 
180 
. 360 . 
... 75 . 
. . . 15 . . 
. 14.9 
The radii in the two last columns are obviously those of a curve approaching 
to an ellipse whose major and minor axes are situated, the one 45° to the right, 
and the other 45° to the left of the plane of the first reflexion. The major 
semiaxis is 22°, and the minor 12°. Hence calling# the variable radius of the 
ellipse, a the greater and b the lesser semiaxis, and & the azimuth, reckoned 
from the lesser axis, in which the radius x is wanted, we shall have 
a b 
X a* cos 2 0 + b s sin 2 0‘ 
When 6 = 45°, 135°, &c. sin 2 0 cos 2 tJ = A and x — —= a ^ ■■ ===. 
By calculating the values of x corresponding to the azimuths in the Table, we 
obtain the numbers in the last column, which are so near the observed numbers 
as to leave no doubt that an ellipse represents the observations. 
If we perform the same experiments with a plate of silver at 7 3°, we shall 
observe, with surprise, that the angle of restoration is the same in all azimuths, 
that is, that the ellipse has merged into the circle. There is a slight deviation 
indeed, just sufficient to show that the circle is slightly oval, but I could not 
measure the amount of it. 
This result arises from the elliptical polarization of silver being very 
nearly circular. If we call (3 the angle of restoration after two reflexions, 
2 R 
MDCCCXXX. 
