Polarization of the Light reflected by the Sky. 103 
TaBLE I.—Light reflected when n is near unity, or equals 1 + dn. 
i A B | 4+2)} 4-23 | Theor. | obs. | Differ. 
A+B 
0° 1-000 1-000 1-000 0-0 0°0 0-0 0-0 
5 1-015 985 1°000 15 1-0 10 0-0 
10 1-063 “939 1001 6-2 4°2 3°5 +0°% 
15 1°149 862 1005} 143 10°0 9-0 4-10 
20 1°282 752 1017| 26-0 18-2 17°5 +0°7 
25 1-482 612 1°047| 41°56 29°0 28°5 +0°5 
30 1-778 1lll 42 41:0 +10 
35 2-221 260 1°240|} ‘79-1 554 56°0 —0°6 
40 2-904 088 1496} 94°5 66°1 67-0 —0°9 
45 4000 000 2-000} 100-0 70-0 72 ia hb 
50 5°857 176 3°016| 94°65 6671 68-0 —1°9 
55 9°239 1-08 5°160 91 554 58°0 —25 
60 16-000 4000 10000} 60-0 42°0 —2°0 
65 31'346 12°952 22°149| 41°5 29-0 30-0 —1°0 
70 73-079 42-884 57°981| 26-0 18°2 18-0 +0°2 
7 222-85 167-16 195-00 4:3 10°0 : +1°5 
80 | 1099°85 971-21 | 1035°53 6-2 42 3-0 +1°2 
85 = |17330°64 |16808°08 |17069°36 15 10 10 0°0 
9 oo oo oo 0-0 0-0 0-0 0°0 
The most important application of Fresnel’s formula is to 
the case of glass where n somewhat exceeds 1°5. The first por- 
tion of Table II. gives in an abreviated form the result of a 
computation, for various values of 2, of A, B, # and the 
polarization of the reflected and refracted rays. When, as 
frequently happens in the case of plates of glass, the light 
passes through several parallel surfaces, a portion of the light 
reflected back by the second surface is again intercepted by 
the first surface. It may readily be proved that if A is the 
amount reflected by a single surface, the amount transmitted, 
including this internal reflection, will be i+¢ a) A’ while if 
no internal reflection took place it would be only (1—A)". In 
Table IL the values of A, B, R and of the polarization, are 
given for 2, 8, and 20 surfaces, corresponding to 1, 4, and 10 
plates of glass. In all these cases the index n=1°565. 
These results are perhaps better shown in figs. 1 and 2, in 
Which abscissas represent values of #, and ordinates percentages 
of the beams reflected by 1, 2, 8, and 20 surfaces. The other 
four curves give the correspondi 
fracted beam, and the polarization of both the reflected an 
refracted beams. When i=0, both the reflected and refracted 
beams are unpolarized. With ten plates of glass about half the 
Am. Jour. — Series, Vou. VII, No. 38.—Fes., 1874. 
