314 
DR. BREWSTER ON THE PHENOMENA AND LAWS 
zation. At angles between 82° 30' and 90° the pencil is only partially polarized 
elliptically ; whereas from 82° 30' to 73° the light has been more than ellipti- 
c-ally polarized, the restoration of it having been begun during the second 
reflexion. Hence, in order to determine the phase for any angle between 
82° 30' and 90°, we must take the sum of the phases for each reflexion, or 2 P ; 
whereas between 82° 30' and 73° we must take the excess of the sum of the two 
phases above 90° or 90° — 2 P. In both cases the pencil has suffered a partial 
elliptic polarization ; — in the former, from the sum of the actions of the two 
reflexions, and in the latter, from their unbalanced actions. The very same 
effects take place between 73° and 57° 16', the other maximum, as between 73° 
and 82^°; and between 57° 16' and 90°, as between 82^° and 90°. 
In the case of three reflexions there are two points or nodes of restoration, 
viz. 78° 8' and 66° 35', the maxima being at 85° 6', 73°, and 48° 38', at each of 
which points the phase is 90°. At 73° the second reflexion restores the ray 
elliptically polarized by the first reflexion, and the third reflexion again pro- 
duces elliptic polarization. At 85° 6' and 48° 38', six reflexions produce a 
restoration of the pencil, and consequently three reflexions must have polar- 
ized the pencil elliptically with a phase of 90°. From 85° 6' to 90°, and from 
48° 38' to 0°, the pencil has been only partially elliptically polarized, and the 
phase at any angle between these will be 3 P. At any angle between 48° 38' 
and 85° 6', the phase will be 2 X 90 — 3 P. 
In general, calling n the number of reflexions, the phase between 90° and 
the nearest maximum, and between 0° and the nearest maximum, will be n P, 
while at all other angles of incidence it will be (w — lx 90) — n P. 
In order to give a general view of the number of points of restoration, and 
of the other phenomena which take place after different numbers of reflexions, 
I have drawn up the following Tables. 
