OF ELLIPTIC POLARIZATION. 
301 
In this manner we obtain the following results. 
No. of Reflexions 
for Elliptic Po- 
larization. 
Angle of Inci- 
dence on 
Silver. 
Angle of Inci- 
dence on 
Steel. 
Inclination of 
Plane, or < p. 
Rotation of 
Plane, or R. 
Phase, or P. 
o 
o / 
o / 
o 
/ 
o 
_ O 
3 
85 6 
85 45 
30 0 
15 
0 
30 = + 
of 90 
H 
83 49 
84 38 
26 15 
18 
45 
37| = tV 
of 90 
2 
82 30 
83 30 
22 30 
22 
30 
45 = 4 
of 90 
H 
78 8 
79 39 
11 15 
33 
45 
67 i= | 
of 90 
i 
73 0 
75 0 
0 0 
45 
0 
90 = 4- 
of 90 
i| 
66 25 
68 53 
11 15 
33 
45 
67|= 1 
of 90 
2 
57 16 
60 2 
22 20 
22 
30 
45 = | 
of 90 
H 
53 17 
56 5 
26 15 
18 
45 
374 == -nr 
of 90 
3 
48 38 
51 24 
30 0 
15 
0 
30 = 1 
of 90 
In the results of the two preceding Tables, where the number of reflexions is 
an integer, it is easily understood how an elliptically polarized ray begins to 
retrace its course, and recover its state of polarization in a single plane, by the 
same number of reflexions by which it lost it : but it is interesting to observe, 
when the number of reflexions is 1^, 2^, 3^, that the ray must have acquired 
its elliptic polarization in the middle of the second and the third reflexion ; that 
is, when it had reached its greatest depth within the metallic surface. It then 
begins to resume its state of polarization in a single plane, and recovers it at 
the end of 3, 5, and 7 reflexions. This stationary point at which the retrograde 
effect commences, may be made to have its position at any depth beneath the 
surface, by changing the angles of some of the reflexions, or by combining 
plates of metal of different polarizing powers. 
The same curious property is exhibited in total reflexions, as I have found 
that the circular polarization can be produced by 2^, 3^, See. reflexions. 
Hitherto we have chiefly examined the phenomena when the reflexions are 
performed either all above or all below the polarizing angle. We shall now 
proceed to the case when one reflexion is made on one side, and one on the 
other side of the maximum polarizing angle. 
When a ray polarized + 45° has been reflected once from steel at an angle of 
85° or of 54°, it has acquired partially the state of elliptic polarization, and to 
such a degree that three reflexions more at the same angle will complete the 
effect. But if the ray partially polarized elliptically by one reflexion at 85° 
suffers a second reflexion at 54°, it does not acquire more elliptic polarization, 
