OF ELLIPTIC POLARIZATION. 
297 
ceding Table has been calculated. The same formula represents also, as it 
should do, the phenomena at the limits of elliptic polarization. In the case of 
circular polarization, where the plane of polarization of the restored ray is 45°, 
we have, 
x = 45°, tan x = 1, and tan <p = tan” x = 1, or <p = 45° 
after any number of reflexions however great. In like manner, in rectilineal 
polarization, where x = 0°, we have <p = 0°, that is, the ray is polarized in the 
plane of reflexion. 
The above formula is suited to any series of reflexions at any angle when the 
value of <p for the first term of the series is known. The value of <p for two reflex- 
ions, the first term of the principal series, can be determined only by experiment, 
and has been given in a former Table for several metals ; but we may deter- 
mine from it the value of <p for the first term of any other series, provided it is 
an even number, in the following manner. Making x — the inclination for 
two reflexions at the maximum polarizing angle, and <p the value of x at any 
number of reflexions 2 n, we shall have, 
tan x + tan n x 
tan <p = ~ 
(A) 
where tan n x is the value of <p at the maximum polarizing angle for 2 n re- 
flexions ; but as no odd number can occur in the principal series, the preceding 
rule will not apply to such numbers. 
The following Table shows the coincidence between the formula and experi- 
ment. 
Silver. 
Inclination of Plane of 
Number of 
Values of 
Angle of 
Polarization. 
Reflexions. 
n. 
Incidence, 
o / 
Observed, 
o / 
Calculated, 
o / 
2 . . 
. l . . 
. 73 0 . . 
. 39 48 . 
. 39 48 
4 . . 
. 2 . . 
. 82 30 . . 
. 37 45 . 
. 3 7 22 
6 . . 
. 3 . . 
. 85 6 . . 
Steel. 
. 35 0 . 
. 35 22 
2 . . 
. 1 . . 
. 75 0 . . 
. 17 0 . 
. 17 o 
4 . . 
. 2 . . 
. 83 30 . . 
. 11 30 . 
. 11 17 
6 . . 
. 3 . . 
. 85 45 . . 
2 q 2 
. 9 30 . 
. 9 30 
