156 Dr. Brewster on the laws which regulate the 
Prop, xxvii. 
If a pencil of homogeneous or coloured light is incident upon 
any transparent body at an angle whose tangent is equal to 
the index of its refraction, every ray of the reflected pencil will 
be completely polarised in the plane of reflexion. 
This proposition is a necessary consequence of those which 
precede it ; and I have also established it by direct experi- 
ments upon diamond and realgar. 
Prop, xxvur. 
If a pencil of homogeneous or coloured light is incident under 
the circumstances described in Prop. XXV., every ray of it zvill 
lose its reflexibility. 
This proposition, which is also deducible from those which 
precede it, has been established by experiment. 
Prop. xxix. 
If a beam of white light suffers more than one reflexion, every ray 
of it will be completely polarised when the angles of incidence are 
of such a magnitude that the sum of the terms of the formulce 
given under Prop. XVII. is equal to 1, the index of refrac- 
tion for the extreme red ray being substituted in place of m 
if the angles are above the polarising angle , and the index of 
refraction for the extreme blue ray if the angles are below the 
polarising angle. 
This Proposition is manifestly deducible from Prop. XVII. 
compared with Prop. XXVII. Calling dm the part of the 
