DR. BREWSTER ON THE LAW OF 
than the extraordinary image, the intensity of each being in the ratio of cos 2 <p 
to sin 2 <p, <p being the angle of inclination, or 33° in the present case. In like 
manner the ordinary image of B will be in the same ratio brighter than its 
extraordinary image, that is, by considering A and B in a state of superposi- 
tion, the extraordinary image of a pencil of light reflected at 80° will be fainter 
than the ordinary image in the ratio of sin 2 33° to cos 2 33°. But this inequality 
in the intensity of the two pencils is precisely what would be produced by a 
compound pencil, part of which is polarized in the plane of reflexion, and part 
of which is common light. When Malus, therefore, and his successors ana- 
lysed the pencil reflected at 80°, they could not do otherwise than conclude 
that it was partially polarized, consisting partly of light polarized in the plane 
of reflexion, and partly of natural light. The action of successive reflexions, 
however, afforded a more precise means of analysis, in so far as it proved that 
the portion of what was deemed natural light had in reality suffered a physical 
change, which approximated it to the state of polarized light ; and we now see 
that the portion of what was called polarized light was only what may be called 
apparently polarized ; for though it disappears, like polarized light, from the 
extraordinary image of the analysing prism, yet there is not a single particle of 
it polarized in the plane of reflexion. 
These results must be admitted to possess considerable interest in them- 
selves ; but, as we shall proceed to show, they lead to conclusions of general 
importance. The quantity of light which disappears from the extraordinary 
image, is obviously the quantity of light which is really or apparently po- 
larized at the given angle of incidence ; and if we admit the truth of the law of 
repartition discovered by Malus, and represented by P 00 = P 0 cos 2 cp, and 
P oe = P 0 sin 2 p, and if we can determine <p for substances of every refractive 
power, and for all angles of incidence, we may consider as established the ma- 
thematical law which determines the intensity of the polarized pencil, whatever 
be the nature of the body which reflects it, — whatever be the angle at which 
it is incident, — whatever be the number of reflexions which it suffers, and 
whether these reflexions are all made from one substance, or partly from one 
substance and partly from another. 
The first step in this investigation is to determine the law according to which 
i reflecting surface changes the plane of polarization of a polarized ray. This 
