29G 
DR. BREWSTER ON THE PHENOMENA AND LAWS 
No. of Reflexions 
from Steel at 75° 
of Incidence. 
3 . . 
State of the Light Reflected. 
Elliptically polarized. 
Inclination of the Plane of 
Polarization. 
Observed. Calculated. 
4 . . 
Restored to light polarized . . 
+ 510.. + 5 22 
5 
Elliptically polarized. 
6 . . 
Restored to light polarized . . 
-20.. — 1 38 
7 ■ • 
Elliptically polarized. 
8 . . 
Restored to light polarized . . 
0 0.. + 0 30 
9 . . 
Elliptically polarized. 
10 . . 
Restored to light polarized . . 
0 0.. - 0 9 
11 . . 
Elliptically polarized. 
12 . . 
Restored to light polarized . . 
00.. +0 3 
Hence it follows, that at every odd number of 
reflexions at the maximum 
polarizing angle the light is elliptically polarized, and at every even number 
it is restored to a single plane of polarization. In circular polarization the 
inclination <p of this plane is always +45°, even after fifty reflexions, as I have 
ascertained by direct experiment ; but in elliptical polarization the inclination 
diminishes at every restoration ; and in the case of steel it is reduced to near 0° 
after eight reflexions, when the light is all polarized in the plane of reflexion ; 
that is, the elliptic polarization gradually diminishes and terminates in recti- 
lineal polarization. 
The value of p, as given in the preceding Table, and consequently the num- 
ber of reflexions when it approaches to 0°, may be deduced from the formula, 
tan <p = tan 0 . tan x. 
After the first reflexion x = +45°, and <p, or the inclination of the plane of 
the ray as restored by the second reflexion, is = —17°, as given by experi- 
ment. Hence the light which suffers the third reflexion, and is thereby ellip- 
tically polarized, is not, as originally, polarized +45°, but only —17°; and 
consequently, when it is restored after the fourth reflexion, the value of <p must 
be such as corresponds to an equality in the values of x and 0, both of them 
being = 17°- Hence the formula becomes, 
tan <p = tan 2 x, or tan = tan n x ; 
» being the number of pairs of reflexions, or half the number of reflexions 
which the restored ray has undergone. In this way the last column of the pre- 
