polarisation of light by reflexion from transparent bodies. 135 
any transparent body, the image reflected by the first surface 
is nearly coincident with the image reflected by the second 
surface, and Malus observed that they were both polarised 
at the same time. As the angles at which the rays are inci- 
dent upon the two surfaces are very different, this result 
appeared quite inexplicable ; but it will be seen from the 
following Propositions, that the simultaneous polarisation of 
the two pencils is a necessary consequence of the general law, 
and derives from that law the most satisfactory explanation. 
Prop. ix. 
When a pencil of light is incident on the second surface of trans- 
parent bodies, at an angle whose co-tangent is equal to the 
index of refraction, the reflected portion will be either wholly 
polarised, or the quantity of polarised light which it contains 
will be a maximum. 
As the images formed by the first and second surfaces of 
a transparent plate are simultaneously polarised, this Propo- 
sition is established by the experimental results in the pre- 
ceding Table. 
Prop. x. 
The angle of polarisation at the second surface of transparent 
bodies, is the complement of the angle of polarisation at the first 
surface. 
As the angle of incidence at the second surface is equal to the 
angle of refraction at the first surface, and as this latter angle 
is, by the Corollary to Prop. IV. equal to the complement of 
the angle of polarisation, it follows, that the two polarising 
angles are complementary to each other. 
