302 
DR. BREWSTER ON THE PHENOMENA AND LAWS 
but it retraces its course, and recovers its state of single polarization. The 
same phenomenon occurs at the following angles. 
Angles of partial Elliptic 
Angles at which it recovers 
Polarization. 
Values of <p. 
its Polarization. 
Values of <p 
1 Reflex, at 87^ • 
o / 
. 36 5 
1 Reflex, at 4 1 . 
o 
. 36 
/ 
11 
85 
. 2 7 28 
54 . 
. 28 
0 
80 . 
. 12 12 
68 . 
. 12 
36 
77 
5 24 
72 . 
5 
59 
75 • 
0 0 
75 . 
0 
0 
It is obvious, by comparing these angles with those in the preceding Table, that 
they correspond, and are those at which equal phases or rotations are produced. 
The effect of two reflexions, at angles of equal phase, upon the inclination I 
of the plane of polarization is shown in the following Table. 
Inclination I of the Plane of 
Polarization. 
Observed. 
Calculated. 
o 
o 
o 
o / 
1 Reflex, at 90 
and 1 at 0 . 
. . 45 . . 
. 45 0 
q*rl 
a 1 
. 30 0 
2 
* * " * 
85 
54 . 
. . 26 . . 
. 26 5 
80 
68 . 
. . 19 . . 
. 20 8 
77 
72 . 
. . 18 . . 
. 17 2 
75 
75 . 
. . 17 . . 
. 17 o 
The last column of the table is calculated by the formula 
I = tan <p (45° — i!) + 1, 
/ being 1 7 °, or the inclination after two reflexions at the maximum polarizing 
angle. 
In the preceding inquiry we have considered only the phenomena when the 
consecutive reflexions are performed in coincident planes. The investigation 
becomes more troublesome, and the results more interesting when the plane of 
the second reflexion is presented in every different azimuth to the ray that is 
cither wholly or partially elliptically polarized by the first reflexion. 
Let a pencil be elliptically polarized by one reflexion from steel at 75°, and 
let the azimuths be reckoned from the plane of this reflexion. We have 
already seen that a second reflexion at 75° in azim. 0° and 180° restores the 
pencil to a single plane of polarization ; but if we turn the plane of the second 
