403 Dr, Brewster on new Properties of light exhibited 
Assuming the numbers in columns 3d and 4th, I have upon 
this principle computed those in the 5th, which are tlie cal- 
culated angles of aberration, and which agree very strikingly 
with the observed angles. 
If we now turn round the mother of pearl 180° so that the 
pole A may be brought into the position of B, the ray ?'s will 
be reflected towards the pole A, fig. 2. and the complement of 
the angle of extraordinary reflection will be equal to the dif- 
ference between the angle of aberration and the complement 
of the angle of ordinary reflection. In this case we shall 
obtain the results given in the following table. 
Angles of 
incidence 
Complement 
of the angle 
of incidence. 
Observed 
angle of 
aberration. 
Complement of 
the angle of 
exti'aordinary 
reflection. 
Calculated 
angle of 
aberration. 
60* 
30" 
4°- 30' 
25°- 30' 
4°- 33' 
55 
35 
4-37 
31 - 23 
3 — 46 
50 
40 
3 - It 
36 - 49 
3 — 16 
45 
45 
2-57 
42—3 
2 — 56 
40 
so 
2 — 38 
47 - 22 
2 — 40 
30 
60 
2 — 16 
57 - 44 
2 — 19 
20 
70 
2—7 
67 - 53 
2-7 
A 
X 
A — X 
X 
By comparing the observed angles of aberration with the 
complements of the angles of extraordinary reflection, we shall 
find that 
sin. X: sin. x'= sin. A'— x' : sin. A — x 
which indicates the same relation as formerly between the 
angles of aberration and extraordinary reflection. Upon this 
principle I have computed the numbers in the 5th column 
which agree very well with the observed angles. 
While the primary pole A is describing a semicircle round 
r till it reaches B, and another semicircle from B to A again. 
