On Polarization of Light by Reflexion. 281 
The first step in this investigation is to determine the law accord- 
ing to which a reflecting surface changes the plane of polarization 
of a polarized ray. This subject was first examined by Matus, but 
not with that success which attended most of his labors. Before I 
was acquainted with what had been done by M. Fresyet, or with 
the experiments of M. Arago on glass and water, I had made a 
number of very careful experiments on the same subject, and had 
represented them by formule founded on the law of the tangents. 
These formule, however, I found to be defective; and I am persua- 
ded, from a very extensive series of experiments, that the formule 
of Fresnet are accurate expressions of the phenomena under every 
variation of incidence and refractive power. If is the angle of in- 
cidence, 2’ the angle of refraction, x the primitive inclination of the 
plane of the polarized ray to the plane of reflexion, and 9 the incli- 
nation to which that plane is brought by reflexion then, according 
to Fresneu, we have : 
cos (1-+7’) 
cos (t—12’) 
When 2 is 45°, as in the preceding observations, then tan e=1, 
cos (1-+-2’) 
cos (2 — vy) 
Tn these formule, which are founded on the law of the tangents, 
i+” is the supplement of the angle which the reflected ray forms 
with the refracted ray; while z—7’ is the angle which the incident 
ray forms with the refracted ray, or the deviation produced by 
refraction. 
These formule have been verified by M. Araco at ten angles of 
incidence upon Glass, and four upon Water; but his experiments 
were made only in the case where 2 is 45°, and where tan w disap- 
pears from the formula. As my experiments embrace a wider range 
of substances, and also the general case where z varies from 0° to 
90°, I consider them as a necessary basis for a law of such exten- 
sive application. 
The first series of experiments which I made was upon Plate 
Glass, in which the maximum polarizing angle was nearly 56° : hence 
I assume the index of refraction to be 1.4826. ‘The following were 
the results: : 
Tan 9 = tan x —; 
and we have T'an oo 
