70 
DIL BREWSTER ON THE LAW OF THE PARTIAL 
Fig. 1. 
analysis exactly like common light ; so that we are entitled to assume such a 
pencil as the representative of natural light, and to consider every thing that 
can be established respecting the one, as true respecting the other. 
In applying this principle to the analysis of the phenomena produced by 
reflexion, I placed the planes of polarization of the compound beam in the 
plane of reflexion ; but though this led to some interesting conclusions, it did 
not develope any general law. I then conceived the idea of making the plane 
of reflexion bisect the right angle formed by the planes of polarization ; and in 
this way I observed a series of symmetrical effects at different angles of inci- 
dence, which threw a broad light over the whole subject. 
In order to explain these results, let AB 
(Fig. 1.) represent the two pencils of oppo- 
sitely polarized light as separated by double 
refraction ; let a b, c d be the directions of 
their planes of polarization, forming a right 
angle aec, and let the plane of reflexion MN, 
of a surface of plate glass, bisect the angle 
uec, so that the planes a b, cd form angles 
of + 45° and — 45° with the plane M N. Let 
a rhomb of calcareous spar have its prin- 
cipal section now placed in the plane of re- 
flexion. 
At an incidence of 90°, reckoned from the perpendicular, the reflected images 
of A and B suffer no change, the angle a e c is still a right angle, and the four 
pencils formed by the calcareous spar are all of equal intensity. As the inci- 
dence however diminishes, the angle a e c diminishes also, and the ordinary and 
extraordinary images of A and B differ in intensity. At an incidence of 80° for 
example, the angle a e c is reduced from 90° to 66° ; at 70° it has been reduced 
to 40°, and at 56° 45', the maximum polarizing angle, it has been reduced to 0°; 
that is, the planes of polarization ab,cd are now parallel. Below the polarizing 
angle, at 50°, the axes are again inclined to each other, and form an angle of 
22°. At 40° they form an angle of 50°, and at 0°, or a perpendicular incidence, 
they are again brought back to their primitive inclination of 90°. Taking MN 
to represent the quadrant of incidence from 90° at M, to 0° at N, the curves, 
90', O', show the progressive change which takes place in the planes of polari- 
