» 
50 Dr. Brewster on new properties of heal, 
represented in Fig. 2. (PI. II .) ; and when the plane of reflection 
is moved round 90° from this position, the surface of the glass 
will be covered with the complementary fringes, the colours 
gradually passing from the one state into the other during the 
rotatory motion of the black glass, in the same manner as in 
crystallized bodies. 
The nature and intensity of the tints are represented by the 
following formulas, which are the same as those which M. Biot 
found for crystallized bodies.* 
p = O -j- E cos. 2 2 a. 
n = E sin. 2 2 a. 
In these formulae P represents the ordinary pencil, and n the 
extraordinary pencil : O is the coloured tint which preserves 
its primitive polarisation, and is not acted upon by the crys- 
tallized glass : E is the complementary tint which has lost its 
primitive polarisation by the action of the glass being polarised 
in an angle equal to 2 a: and a is the azimuthal angle which 
the axis of the plate forms with the plane of primitive pola- 
risation. 
Proposition V. 
The coloured fringes mentioned in the preceding Proposition, and 
represented in Fig . 2. consist of six different sets, two exterior, 
two interior, and two tei'minal sets. The exterior sets occupy 
the edges , the interior sets the middle, and the terminal sets 
the extremities of the glass plate , and each set is separated from 
its adjacent set by a deep black fringe . 
These different sets of fringes are represented in Fig. 2. 
(Pl. II.) where CDEF is the glass plate, and CD the edge of 
it which rests upon the hot iron. The first exterior or lateral 
* See Biot’s Rechcrches sur la polarisation dc la lumiere, p. 21. 
