On Polarization of Light by Reflexion. 291 
very same laws are applicable to their second surfaces, provided that 
the incident light has not suffered previous or subsequent refraction 
from the first surface. The sine of the angle at which g or Q hasa 
certain value by reflexion from the second surface, is to the sine of 
the angle at which they have the same value at the first surface, as 
unity. is to the index of refraction. Hence 9 and Q may be deter- 
mined by the preceding formule after any number of reflexions, even 
if some of the reflexions are made from the first surface of one body 
and the second surface of another. : 
When the second surface is that of a plate with parallel or inclined 
faces, its action upon light presents curious phenomena, the law of 
which I have determined. I refer of course to the action of the sec- 
ond surface at angles less than that which produces total reflexion. 
This action has hitherto remained uninvestigated. It has been 
hastily inferred, however, from imperfect data; and the erroneous 
inference forms the basis of some optical Jaws, which are considered 
to be fully established. 
Among the various results of the preceding investigation, there is 
one which seems to possess some theoretical importance. If we con- 
sider polarized rays as those whose planes of polarization are paral- 
lel, then it follows that light cannot be brought into such a state by 
any number of reflexions, or at any angle of incidence, excepting at 
the angle of complete polarization. At all other angles the light which 
seems to be polarized, by disappearing from the extraordinary image 
of the analysing rhomb, is distinguished from really polarized light, 
by the property of its planes of polarization forming an angle with 
each other and with the plane of reflexion. At the polarizing angle, 
for example, of 56° 45” in glass, the light reflected is i 9.5 rays, and 
it is completely polarized, because the planes of polarization of all the 
rays are parallel; but at an angle of incidence of 80°, where 392 
rays are reflected, no fewer than 157 appear to be polarized, though 
their planes of polarization are inclined 66° 26/ to each other, or 33/ 
13’ to the plane of reflexion. This appearance of polarization, when 
‘the rays have only suffered a displacement in their planes of polariza- 
tion from an angle-of 90°, which approximates them to the state of 
polarized light, arises from the law which regulates the repartition of 
_ Polarized light between the ordinary and extraordinary images produ- 
ced by double refraction, and shows that the analysing crystal is not 
sufficient to distinguish light completely polarized from light in a state 
of approach to polarization. The difference, however, between these 
