78 
DR. BREWSTER ON THE LAW OF 
I Ience we have 
/sin* (?' — i') 
\sin*(* + z 1 ) 
COS 2 X + 
tan 9 (z — z 1 ) . „ 
r — o ; -. r \ Sin 2 
tan ( z 4- z') 
tan x 
cos (Z + V) 
— 2 
cos ( i 
zJLLY 
- i')) 
1 + 
' . cos (i + i 
tan x Y- rs 
\ COS ( l — z') 
! ! 1 ) 
i')) 
This formula is equally applicable to a single pencil of polarized light of the 
same intensity as the pencil of partially polarized light. In all these cases it 
expresses the quantity of light really or apparently polarized in the plane of 
reflexion. 
In order to show the quantity of light polarized at different angles of inci- 
dence, I have computed the following table for common light, and suited to 
glass in which m = 1.525. 
Plate Glass. 
Angle of 
Incidence 
i. 
Angle of 
Refraction 
i'. 
Inclination of Plane 
of Polarization to 
Plane of Reflex- 
ion, Q. 
Quantity of Light 
reflected out of 
1000 Rays. 
Quantity of Pola- 
rized Light Q, 
Ratio of Polar- 
ized to Reflected 
Light. 
O 
0 
/ 
0 
O / 
0 0 
45 6 
43.23 
0 
0 
10 
0 
6 32 
43 51 
43.39 
1.74 
0.04000 
20 
0 
12 58 
40 13 
43.41 
7.22 
0.16618 
25 
0 
16 5 
37 21 
43.64 
11.6 
0.26388 
30 
0 
19 81 
33 40 
44.78 
17-25 
0.3853 
35 
0 
22 6 
29 8 
46.33 
24.37 
0.5260 
40 
0 
24 56 
23 41 
49*10 
33.25 
0.6773 
45 
0 
27 37± 
17 22| 
53.66 
44.09 
0.82167 
50 
0 
30 9 
10 18 
61.36 
57.36 
0.9360 
56 
45 
33 15 
0 0 
79-5 
79-5 
1.000 
60 
0 
34 36 
5 4| 
93.31 
91.6 
0.9628 
65 
0 
36 28 
12 45 
124.86 
112.7 
0.90258 
70 
0 
38 2 
18 32 
162.67 
129.80 
0.79794 
75 
0 
39 18 
26 52 
257.26 
152.34 
0.59154 
78 
0 
39 54 
30 44 
329.95 
157.67 
0.47786 
79 
0 
40 4 
31 59 
359.27 
157.69 
0.43892 
80 
0 
40 13 
33 13 
391.7 
156.6 
0.40000 
82 
44 
40 35 
36 22 
499.44 
145.4 
0.29112 
84 
0 
40 42 
38 2 
560.32 
134.93 
0.2408 
85 
0 
40 47 
39 12 
6l6. 28 
123.75 
0.2008 
86 
0 
40 51 
40 22.7 
676.26 
108.67 
0.16068 
87 
0 
40 54 
41 32 
744.11 
89.83 
0.12072 
88 
0 
40 57£ 
42 42 
8 19.9 
65.9 
0.0804 
89 
0 
40 58 
43 51 
904.81 
36.32 
0.04014 
90 
0 
40 58 
45 0 
1000.0 
0 
0.0000 
As the preceding formula is deduced from principles which have been either 
established by experiment or confirmed by it, it may be expected to harmonize 
