300 
Dll. BREWSTER ON THE PHENOMENA AND LAWS 
state of partial polarization as if common light had been reflected either at an 
angle of 45° or 68° from a surface of glass. Consequently in the formula * 
Q = 1 — 2 sin 2 <p, we have <p = 17° and Q = 0.829. 
Hitherto we have considered elliptical polarization as produced only at the 
maximum polarizing angle. It may be produced, however, by a sufficient 
number of reflexions at any given angle either above or below the maximum 
polarizing angle, as appears from the following Table, in which the reflexions 
are made from two parallel plates of steel. 
No. of Reflexions 
from Steel at which 
Elliptic Polarization 
is produced. 
No. of Reflexions at 
which the Pencil is re- 
stored to a single Plane. 
Angles of Incidence. 
Calculated. 
Observed. 
3, 9, 15, &c. 
6, 12, 18, &c. 
o / 
85 45 
O / 
86 0 
H, 7 b 12 b &c. 
5, 10, 15, &c. 
84 38 
84 0 
2, 6, 10, &c. 
4, 8, 12, &c. 
83 30 
82 20 
lb 4b 7b &c. 
3, 6, 9, &c. 
79 39 
79 0 
1, 3, 5, &c. 
2, 4, 6, &c. 
75 0 
75 0 
lb 4i, 7b &c. 
3, 6, 9, &c. 
68 53 
67 40 
2, 6, 10, &c. 
4, 8, 12, &c. 
60 2 
60 20 
Ol 7 1 1 Ql Src 
5, 10, 15, &c. 
56 5 
56 25 
3, 9, 15, &c. 
6, 12, 18, &c. 
51 24 
52 20 
The numbers given in the third column are calculated by the following me- 
thod. The relation of the preceding phenomena to the angle of maximum 
polarization is obvious ; and if we consider the nature of the formula, tan <p = 
COS (? -f- 
co S - (T^? p we shall see that the angles at which the rectilineal polarization of 
the primitive pencil is destroyed have a reference to the rotation which the 
reflecting surface produces in the plane of polarization. The angles indeed in 
the third column, at which similar effects are produced above and below 7 5°, 
are those at which <p has equal values. This is a very important relation, and 
enables us to determine the phase P of the two inequal portions of oppositely 
polarized light, by the interference of which the elliptic polarization is produced. 
It may be expressed by P = 2 R. 
But R = 45° — <p, 
Hence P = 90° — 2 <p. 
tan <p = 
cos (i + i') 
cos (i — i')’ 
•See my Paper “ On the Law of the Partial Polarization of Light by Reflexion,’’ supra, p. 7G. 
