288 On Polarization of Light by Reflexion. 
the maximum polarizing angle of the glass *. In order to compare 
this principle with the formula, I found that in Water No. 4. the an- 
gle which polarizes almost exactly the same proportion of light as the 
angle of 86° 31’, is 15° 10’, the value of » 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. Araco cannot be regarded as correct, and can- 
not therefore be employed, as he sapresa to determine the angle 7 
complete polarizationt. 
The application of the law of intensity to the phenomena of the po-" 
larization of light by successive reflexions, forms a most interesting sub- 
ject.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 re- 
_peated. All my fellow laborers, indeed, have overlooked them as 
insignificant, and have even pronounced the results which flow from 
them to be chimerical and unfounded. Those immutable truths, how- 
ever, which rest on experiment, must ultimately have their triumph ; 
and it is with no slight satisfaction, that, after fifteen years of unre- 
mitted labor, Iam 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 trans- 
parent surface, 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 2 =45°, but it is partially polarized light in which a= 
6° 45’. In computing therefore the effect of the second reflexion, 
cos (2-2) 
but, 
cos (1 — A) 
as the value of a is always in the same ratio to the value of 9, how- 
ever great be the number of reflexions, we have tan = tan"9 for. 
the inclination 4 to the plane of reflexion produced by any number 
of reflexions n, 9 being the inclination for one reflexion. Hence 
when @ is given by observation, we have tangp={/o0. The formula 
we must take the general formula tan o = tan ie, 
* 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 wher m==1.000; so that its error 
increases with the refractive power. 
