OF ELLIPTIC POLARIZATION. 
295 
The following experiments were made with plates of pure silver, in which 
the inclination <p was 39° 48', when the inclination x of the plane of polariza- 
tion was 45°. 
Inclination x of the Plane 
of primitive Polarization 
to Plane of Reflexion. 
Observed Inclination of the 
restored Ray to the Plane 
of Reflexion or i p. 
Inclination <p calcu- 
lated by the 
Formula. 
+ 90 . . . 
. 
0 ' 
. — 90 0 . . . 
o / 
. . — 90 0 
85 . . . 
• 
84 36 . . . 
84 0 
75 . . . 
• 
74 10 . . . 
72 10 
65 . . . 
• 
63 51 . . . 
60 46 
55 . . . 
. 
52 18 . . . 
49 57 
45 . . . 
d 
= 39 48 . . . 
39 48 
35 . . . 
• 
32 23 . . . 
30 28 
25 . . . 
• 
23 10 . . . 
21 14 
15 . . . 
. 
13 16 . . . 
12 35 
5 . . . 
• 
4 40 . . . 
4 10 
0 . . . 
0 0... 
0 0 
Calling 0 the inclination or value of <p at 45°, we may represent these obser- 
vations by the formula, tan <p — tan 6 tan x, and the actual change of the plane 
of polarization, or R, will be R = x + 
When <p is given, tan x = and when <p = 45°, and consequently tan <p = 1, 
we have, cot x = tan d, and x — 90° — 0. 
Since light polarized +45° is elliptically polarized by one reflexion from 
steel at 75°, and is restored to light polarized —17° by a second reflexion at 
75°, it is clear that a third reflexion at 75° will again polarize it elliptically, 
while a fourth reflexion at 75° will again restore it to light polarized + 0 , 
0 being a quantity less than 17°, and given by the preceding formula. The 
same effects will be reproduced with different numbers of reflexions, as in the 
following Table. 
No. of Reflexions 
from Steel at 75° State of the Light Reflected, 
of Incidence. 
1 . . Elliptically polarized. 
2 . . Restored to light polarized 
MDCCCXXX. 2 Q 
Inclination of the Plane of 
Polarization. 
Observed. Calculated. 
o i o 
. -17 0 . . -17 
