polarisation of light by reflexion from transparent bodies. 151 
Direct light -f- 
Light reflected 
at an angle of 4 0 
The negative part 
P 
56° 45 ' 

* ( 56 ° 45 ') 
of the reflected beam may be represented 
in a similar manner. The particle of direct light being 
already polarised, will suffer no change by the reflexion 
( Prop. XVIII. ) The particle being susceptible of polari- 
sation by reflexion at an angle of i° will also be polarised at 
any angle above i°, and will therefore come into the state of 
~ . In like manner the particles ~ will all be pola- 
rised, and assume the state represented by The particle 
being susceptible of polarisation only at an angle of 5 0 or 
more will not be polarised at 4 0 , but will be brought into a 
state very near that of polarised light. It will therefore be 
represented by % being a fractional coefficient, always less 
than 1, to be determined by the formulas in Prop. XVII. For 
the same reason all the other particles will be brought into a 
state nearer that of perfect polarisation, and will be represented 
by and— r-A— Tv* 
J x 6 ° *(56° 45) 
Cor. 2. In general, all the particles of a direct beam of light 
whose denominator is equal to or less than the angle of inci- 
dencewill be brought by reflexion into the state of while all 
the particles whose denominator exceeds the angle of inci- 
dence will be brought into a state which may be found by 
multiplying their state in the direct beam by z being de- 
termined by Prop. XVII. 
