ELLIPTIC POLARIZATION OF LIGHT BY REFLEXION. 
43 
ent on the thickness traversed), or it becomes 
sin <p sin (v t — x + g) + d) + cos <p sin (v t — x) + = E'. 
The parts remaining after analysation in a plane A perpendicular to P will then be, 
0 cos (45 — <p) — E' sin (45 — <p). 
These upon expansion are at length reducible to the form 
2 7T 2 7T 
H sin — (vt — x) -{- K cos — (v t — x ), 
whence, after reduction, we obtain 
H 2 + K 2 = 1 — sin 2 2 <p cos § — cos 2 <p sin sin d — cos 2 2 <p cos § cos 6, 
which expresses the intensity of light at any part of the rings, assigned by <p and 6 ; 
and is susceptible of variations according to the value of §, or the changes in retarda- 
tion which may arise from differences in the nature of the metallic films, as in the 
following Table : — 
Values 
of 
Expression for the intensity : 6 given. 
Nature of the rings. 
For <p in general. 
** ~ { 180°. 
/ 45°. 
t 225°. 
J 90°. 
1270°. 
ri35°. 
1315°. 
0 
1 — sin 2 2 cp — cos 2 2 <p cos 0 
1 — cos 0 . . 
0 
1 — cos 0 . . 
0 
Dark-centred, circular. 
it 
~2 
1 — cos 2 <p sin 0 
1 — sin 0 . . 
1 
1 + sin 0 . . 
1 
Dislocated (1). 
7t 
1 + sin 2 2 <p + cos 2 2 <p cos 0 
1 + cos 0 . . 
2 
1 + cos 0 . . 
2 
Bright-centred, circular. 
3 7 r 
IT 
1 + cos 2 <p sin 0 
1 + sin 0 ■ • 
1 
1 — sin 0 . . 
1 
Dislocated opposite way to( 1 ). 
2 it 
1 — sin 2 2 <2> — cos 2 2 0 cos 0 
1 — cos 0 . . 
0 
1 — cos 0 . . 
0 
Dark-centred, circular. 
&c. 
&c. 
&c. 
&c. 
&c. 
&c. 
&c. 
These changes will accord with those observed through one order of tints, if the 
increase of from 0 to 2 t correspond to an increment of one wave length, or if 
e = and k be made successively = 0, &c. 
