138 
I)R. BREWSTER ON THE LAWS OF 
Angles of 
Angles of 
Rotation 
Inclination 
Inclination 
Incidence. 
Refraction. 
observed. 
observed. 
calculated. 
Difference. 
0° 
. 0° 
0' 
. 0° 
0' 
. 45° 
0' 
. 45° 
0' 
10 
. 6 
36^ 
. 0 
13 
. 45 
13 
. 45 
6 
. +0° 
7' 
20 
. 13 
5 
. 0 
27 
. 45 
27 
. 45 
25 
+0 
2 
25 
. 16 
15 
. 0 
32 
. 45 
32 
. 45 
40 
. -0 
8 
30 
. 19 
20 
. 0 
40 
. 45 
40 
. 46 
0 
. -0 
20 
35 
22 
19 
. 1 
12 
. 46 
12 
. 46 
25 
. —0 
13 
40 
. 25 
10 
. 1 
30 
. 46 
30 
. 46 
56 
. —0 
26 
45 
• 27 
55 
. 1 
42 
. 46 
47 
. 47 
34 
. -f 0 
47 
50 
. 30 
29 
2 
48 
• 47 
42 
. 48 
24 
. -0 
42 
55 
. 33 
52 
. 3 
54 
. 48 
54 
. 48 
59 
. — 0 
5 
60 
. 35 
0 
. 5 
7 
. 50 
7 
. 50 
36 
. — 0 
29 
65 
. 36 
53 
. 6 
48 
. 51 
48 
. 52 
7 
. —0 
19 
70 
. 38 
29 
. 8 
7 
. 53 
7 
. 53 
59 
. -0 
52 
75 
. 39 
45 
. 9 
55 
. 54 
55 
. 56 
18 
. — 1 
23 
80 
. 40 
42 
. 12 
10 
• 57 
10 
. 59 
5 
1 
55 
85 
. 41 
17 
. 15 
45 
. 60 
45 
. 62 
24 
. — 1 
39 
86 
. 41 
21 
. 16 
39 
. 61 
39 
. 63 
9 
. — 1 
30 
90 
. 41 
28 
66 
19 
The last column but one of the Table was calculated by the formula, 
Cot 0 = (cos ( i — i' )) 2 
n being in this case 2. The conformity of the observed with the calculated 
results is sufficiently great, the average difference being only 41'. The errors 
however being almost all negative, I suspected that there Avas an error of ad- 
justment in the apparatus ; and upon repeating the experiment at 80°, the point 
of maximum error, I found that the inclination was fully 58° 40', giving a dif- 
ference only of 25' in place of 1° 55'. I did not think it necessary to repeat 
all the observations ; but I found, by placing the analysing rhomb at the calcu- 
lated inclinations, that the extraordinary image invariably disappeared, the 
best of all proofs of the correctness of the formula. 
In these experiments x — 45° and cot x = 1 ; but in order to try the formula 
when x varied from 0° to 90°, I took the case where the angle of incidence was 
80° and <p = 58° 40' when x = 45°. The following were the results. 
