THE PARTIAL POLARIZATION OF LIGHT BY REFLEXION. 
79 
with the results of observation. At all the limits where the pencil is either 
wholly polarized or not polarized at all, it of course corresponds with experi- 
ment : but though in so far as I know there have been no absolute measures 
taken of the quantity of polarized light at different incidences, yet we are for- 
tunately in possession of a set of experiments by M. Arago, who has ascertained 
the angles above and below the polarizing angle at which glass and water 
polarize the same proportion of light. In no case has he measured the absolute 
quantity of the polarized rays ; but the comparison of the values of Q at those 
angles at which he found them in equal proportions, will afford a test of the 
accuracy of the formula. This comparison is shown in the following table, in 
which col. 1. contains the angles at which the reflecting surface polarizes equal 
proportions of light ; col. 2. the values of <p or the inclination of the planes of 
polarization ; and col. 3. the intensities of the polarized light computed from 
the formula. 
Angles of 
Incidence i. 
Inclination of Planes of 
Polarization to M N, or <p. 
Proportion 
Polarized Light 
Glass : No. 1. 
f 82° 48' . 
{24 18 . 
. . . 37° 33' . . 
... 37 21 . . 
. . .2572 
. . .2637 
No. 2. 
("82 5 . 
... 36 47 • . 
. . .2828 
{26 6 . 
... 36 0 . . 
. . .3090 
No. 3. 
f78 20 . 
... 32 38 . . 
. . .4186 
\29 42 . 
... 33 1 . . 
. . .4064 
Water : No. 4. 
f 86 31 . 
\ 16 12 . 
... 41 54 . . 
... 41 27 . • 
. . .1080 
. . .1236 
The agreement of the formula with experiments made with as great accuracy 
as the subject will admit must be allowed to be very satisfactory. The differ- 
ences are within the limits of the errors of observation, as appears from the 
following table : 
Deviations from Part of the 
Experiment. whole Light. 
Glass: No. 1. 0.0065 .... T -|^ r 
No. 2. 0.0262 . . . . -gV 
No. 3. 0.0122 . . . . -gV 
Water: No. 4. 0.0156 .... 
M. Arago has concluded, from the experiments above stated, that equal 
proportions of light are polarized at equal angular distances from the angle of 
