58 
SIR DAVID BREWSTER ON THE PHENOMENA OF THIN PLATES. 
then the complements of the azimuths of the polarized light being set off from the 
corresponding angles of incidence on each side of A B, the curves A C B, A C B 
passing through these points will show at what angles of incidence and azimuth the 
rings disappear, in consequence of the planes of polarization of the two pencils being 
at these places rectangular. 
At all incidences, and in all azimuths within the shaded space A C B C, the white- 
centred rings are seen, and at all other azimuths and incidences the black-centred 
rings are seen. 
2. Fluor Spar and Water . — I have taken this combination as a specimen of the 
phenomena which take place at some incidences less than 90°, when the refracted 
ray falls on the second surface of the film, at angles greater than its polarizing angle. 
The following Table shows the values of x and their complements : — 
Angles of Incidence. 
Azimuths. 
Complements. 
53 11 
o / 
0 0 
O / 
0 0 
55 
82 35 
7 25 
60 
77 47 
12 13 
63 
76 54 
13 6 
65 
76 41 
13 19 
67 
77 6 
12 54 
70 
78 9 
11 51 
75 
82 0 
8 0 
78 
88 41 
11 9 
78 4 
90 0 
0 0 
80 
83 28 
6 32 
85 
77 31 
12 29 
90 
74 14 
15 46 
By projecting these values, as is done in fig. 5, we obtain a double set of curves 
which unite at D, where the angle of incidence is 78° 4', at which the refracted ray 
falls upon the second surface at its polarizing angle. 
At all incidences, and in all azimuths within the shaded portions of the figure 
Z A Z D, D C B C, the white-centred rings are seen. At all azimuths and incidences 
corresponding with the outlines of the curves Z D Z, D C B C, the rings disappear ; 
and at all azimuths and incidences without the shaded portions of the figure, the 
black-centred rings are seen*. 
* No reference is made in these figures to the phenomena which are seen by using both polarized light 
and the analyzing rhomb. 
St. Leonard's , St. Andrew's, 
April 8, 1841. 
