so 
DR. RREWSTER ON THE LAW OF 
complete polarization. Tims in Glass No. 1. the mean of 82° 48' and 24° 18' 
i» 53° 33', which does not differ widely from the maximum polarizing angle, or 
which M. Arago considers as the maximum polarizing angle of the glass*. 
In order to compare this principle with the formula, I found that in Water 
No. 4. the angle which polarizes almost exactly the same proportion of light as 
the angle of 86° 31', is 15° 10', the value of <p being 41° 54' at both these angles ; 
but the mean of these is 50° 50' in place of 53° 11'; so that the rule of M. Arago 
cannot be regarded as correct, and cannot therefore be employed, as he pro- 
poses, to determine the angle of complete polarization 
The application of the law of intensity to the phenomena of the polarization 
of light by successive reflexions, forms a most interesting subject of research. 
No person, so far as I know, has made a single experiment upon this point, 
and those which I have recorded in the Philosophical Transactions for 1815, 
have, I believe, never been repeated. All my fellow labourers, indeed, have 
overlooked them as insignificant, and have even pronounced the results which 
flow from them to be chimerical and unfounded. Those immutable truths, 
however, which rest on experiment, must ultimately have their triumph ; and 
it is with no slight satisfaction, that, after fifteen years of unremitted labour, I 
am enabled not only to demonstrate the correctness of my former experiments, 
but to present them as the necessary and calculable results of a general law. 
When a pencil of common light has been reflected from a transparent sur- 
face, at an angle of 61° 3' for example, it has experienced such a physical 
change, that its planes of polarization form an angle of 6° 45' each with the 
plane of reflexion. When it is incident on another similar surface at the same 
angle, it is no longer common light in which x — 45°, but it is partially pola- 
rized light in which x =6° 45'. In computing therefore the effect of the second 
( cos (i -f- i j\ 
cos (i "—~F) ) ’ ^ Ut ’ 
as the value of x is always in the same ratio to the value of tp, however 
great be the number of reflexions, we have tan 0 = tan" <p for the incli- 
nation 0 to the plane of reflexion produced by any number of reflexions n, 
* Hence we have assumed m = 1.428, the tangent of 55°, in the preceding calculations, 
t It is obvious that the rule can only be true when m — 1.000; so that its error increases with 
the refractive power. 
