158 Dr. Brewster on the action of 
perfect crystals, or to communicate to artificial faces that high 
polish which nature often exhibits, I might have obtained a 
more complete generalisation of the preceding phenomena. 
Limited, however, as the investigation has been by these 
causes, it still presents us with several views of great generality 
and interest. 
First. The force of double refraction and polarisation ex- 
tends without the surface of crystals, and within the sphere 
of the force which produces partial reflection. 
Second. The change in the angle of polarisation produced 
by the interior force, depends on the inclination of the re- 
flecting surface to the axis of the crystal, and also on the 
azimuthal angle which the plane of reflection forms with the 
principal section. 
In any given surface, where A and A u are the minimum 
and maximum polarising angles, viz. in the azimuth of o° and 
90°, the polarising angle A' at any intermediate azimuth &, 
may be found by the formula 
A'= A -f- Sin. 2 u (A"-— A). 
In the rhomboidal surfaces of calcareous spar 
A"— A =138'. 
Third. The change in the direction of the polarisation 
must be produced after the ray has suffered reflection ; for if 
the change preceded reflection, the reflecting force would 
have polarised it in the plane of reflection, whatever had been 
the direction of its previous polarisation. 
Fourth. The change in the direction of the polarisation 
depends upon the angle which the incident ray forms with 
the axis of the crystal, and takes place' in such a manner 
that if 
