On Polarization of Light by Reflexion. QUT 
Arr. IV.—On the law of the partial polarization of light by reflex- 
ton; by Davin Brewster, LL.D. F.R.S. L&E. 
Read before the a Society, February 4, 1830. 
In the year 18151 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 un- 
derwent a sufficient number of reflexions, either at angles wholly 
above or wholly below the maximum polarizing angle, or at angles 
partly above and partly below that angle; and it was scarcely possi- 
ble to resist the conclusion, that the light not polarized by the first re- 
flexion had suffered a physical change at each action of the reflect- 
ing force which brought it nearer and nearer to the state of com- 
plete polarization. This opinion, however, which I have always re- 
garded as demonstrable, appeared in a different light to others. Gui- 
ded probably by an experimental result, apparently though not really 
hostile to it, Dr. Youne and MM. Biot, Araco, and FResnet, 
have adhered to the original opinion of Matus, that the reflected 
and refracted pencils consist partly of light wholly polarized, and 
partly of light in its natural state ; and more recently Mr. HerscHen 
has given the weight of his opinion to the same view of the sub- 
ject. 
Under these circumstances I have often returned to the investiga- 
tion with renewed zeal; but though the frequent repetition of my 
experiments has more anid more eeayinced 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 funda- 
mental branch of the science of polarization. 
If we consider a pencil of natural light as divided into two pen- 
cils polarized in rectangular planes by the action of a doubly refract- 
ing crystal, and conceive the light of these two pencils to return back 
through the crystal, it will obviously emerge in the state of natural light. 
When we examine the pencil thus recomposed, or when we exam- 
ine a pencil consisting of two oppositely polarized pencils superpo- 
sed, we shall find that they comport themselves under every analysis 
Vou. XXII.—No. 2. 36 
