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III. On the law of the partial polarization of light by reflexion. By 
David Brewster, LL.D. F.R.S. L. 8$ E. 
Read February 4, 1830. 
In the year 1815 I communicated to the Royal Society a series of experiments 
on the polarization of light by successive reflexions, which contain the germ 
of the investigations, the results of which I now propose to explain. 
From these experiments it appeared that a given pencil of light could be 
wholly polarized at any angle of incidence, provided it underwent a sufficient 
number of reflexions, either at angles wholly above or wholly below the maxi- 
mum polarizing angle, or at angles partly above and partly below that angle ; 
and it was scarcely possible to resist the conclusion, that the light not polarized 
by the first reflexion had suffered a physical change at each action of the 
reflecting force which brought it nearer and nearer to the state of complete 
polarization. This opinion, however, which I have always regarded as demon- 
strable, appeared in a different light to others. Guided probably by an expe- 
rimental result, apparently though not really hostile to it. Dr. Young and 
MM. Biot, Arago, and Fresnel, have adhered to the original opinion of Malus, 
that the reflected and refracted pencils consist partly of light wholly polarized, 
and partly of light in its natural state ; and more recently Mr. Herschel has 
given the weight of his opinion to the same view of the subject. 
Under these circumstances I have often returned to the investigation with 
renewed zeal ; but though the frequent repetition of my experiments has more 
and more convinced me of the truth of the conclusions which I drew from them, 
yet I have not till lately been able to place the subject in a satisfactory aspect, 
and to connect it with general laws, which give a mathematical form to this 
fundamental branch of the science of polarization. 
If we consider a pencil of natural light as divided into two pencils polarized 
in rectangular planes by the action of a doubly refracting crystal, and conceive 
the light of these two pencils to return back through the crystal, it will obvi- 
ously emerge in the state of natural light. When we examine the pencil thus 
recomposed, or when we examine a pencil consisting of two oppositely polarized 
pencils superposed, we shall find that they comport themselves under every 
