14 6 Dr. Brewster on the laws which regulate the 
Let it be required, for example, to ascertain what effect will 
be produced upon a ray of light by four reflexions at the fol- 
lowing angles. t 
Above the polarising angle 
Below the polarising angle 
77 4° 
7° 9 
50 26 
35 18 
The values of N and n in the Table corresponding to these 
angles are, 27, 6, 2, 10, and 64, and therefore we have 
_Lj.J_j.l4J.. -S - 2 . 6 2i- 
2 ~ 6 ' 2 ^ 10 3240 > 
{ 
{ 
which being less than 1, the ray will not be polarised, but 
will require another reflexion either at 6g° 1' or 41 0 43', for 
the values of N and n corresponding to these angles are both 
5 and -f- — — = = 1 very nearly. 
u 5 1 3H 0 IOZO J J 
The formulae in the preceding proposition are equally ap- 
plicable to the second surfaces of transparent bodies, and to 
the separating surfaces of different media, —• > and — being in 
these cases substituted in place of m. 
Prop, xviii. 
When a ray of light is once completely polarisedy its polarisation 
will suffer no change , and the ray will preserve all its optical 
properties after any number of reflexions at any angle in the 
plane in which it was polarised, or after any number ofrefractions 
in a plane at right angles to that in which it was polarised . 
If a ray is polarised by reflexion in the plane of the hori- 
zon, and is afterwards reflected at various angles in the plane 
of the horizon, one of the images will always vanish in the 
same position of the prism, as if it had not suffered a second 
