10 REPORT—1857. 
principal azimuth, succeeded, without any photometric experiment, in determining the 
quantity of light reflected from the surface of metals, Going even still further, 
M. Cauchy calculated this same quantity of light for all the incidences in cases 
where the primitive ray would be supposed to be decomposed into two polar rays at 
right angles, the one parallel and the other perpendicular to the plane of incidence. 
Thus,—lst, indicating by Ii the intensity of the reflected ray when it is polarized 
in a direction parallel to the plane of incidence, and by Ip the intensity of the re- 
flected ray when it is polarized perpendicularly to the plane of incidence, supposing 
the ray to fall under the principal incidence, and taking as unity the intensity of the 
incident ray, M. Cauchy found— 
For silver ,....scceesees Arete sexervg li = 0°96 Ip = 0°79 
For mercury ...... Cems cep ste Giwecceaa li = 0°94 Ip = 0°46 
For the metal of specula .......csseeeeeee li =.0°90 Ip = 0°36 
For steel ....csc0esseee- Sse oqeeecgseecvecsece li = 0°85 Ip = 0:23 
2. Taking silver alone into consideration, but supposing the ray to fall by turns 
under the incidences 0°, 10°, 30°, 50°, 73°, 74°, M. Cauchy found that the quantities 
of light reflected were— 
Under the incidences 0° 10° 30° 50° 132 74° 
Ii = 0°548 0°553 0°596 0°693 0°814 0°859 
Ip = 0°548 0°543 0°499 0°402 0°261 0°232 
This being settled, the following is the mode of reasoning, by which, we believe, 
all doubt may be removed as to the truth of the hypothesis which supposes that the 
luminous vibrations are perpendicular to the plane of polarization, and as to the 
falsity of that according to which the vibrations are parallel to this plane. 
I. Of the two rays polarized at right angles, which we have hitherto considered, 
one has its vibrations parallel, and the other has them’perpendicular to the plane of 
incidence and to the indication of this plane upon the plane of reflexion. 
If we ask ourselves which of them must be least extinguished in the act of re- 
flexion, which, when reflected must exhibit the greatest intensity, we shall answer 
without hesitation, that of which the vibrations are parallel to the plane of the re- 
flecting surface, as it penetrates less into the metallic medium, and undergoes less of 
its influence. On the other hand, M. Cauchy has proved that the ray Ii, polarized 
in a direction parallel to the plane of incidence, is that which is most reflected : 
consequently it is for this ray Ii that the vibrations are parallel to the reflecting 
surface, or to the plane of reflexion; but vibrations parallel to the reflecting surface 
are at the same time vibrations perpendicular to the plane of incidence, and conse- 
quently perpendicular to the plane of polarization, which for the ray Ii coincides 
with the plane of incidence; therefore for the ray Ii polarized in the plane of inci- 
dence the vibrations are perpendicular to the plane of polarization. If we reasoned 
upon the ray Ip, we should also say that it is the ray which is reflected with the 
least intensity, therefore it is that of which the vibrations are oblique to the reflect- 
ing surface, and at the same time perpendicular to the indication of the plane of 
incidence,—therefore, for the ray polarized perpendicularly to the plane of inci- 
dence, the vibrations are parallel to that plane, or perpendicular to the plane of 
polarization. 4 
II. Of the two rays polarized at right angles, one is of such a nature, that as the 
incidence increases, the intensity after reflexion remains very nearly constant, and 
increases very little in proportion as the incidence increases; the other, on the con- 
trary, is such, that its-intensity after reflexion goes on diminishing more and more. 
Now is it not evident that the ray which must sensibly retain the same intensity 
after reflexion, is the ray of which the vibrations are parallel to the plane of reflexion 5 
that, on the contrary, the ray which becomes extinguished by degrees when the in- 
cidence increases, is the one whose vibrations are in the plane of incidence, perpen- 
dicular to the direction of propagation, and to the intersection of the planes of in- 
cidence and reflexion ; since these vibrations, being at first parallel to the plane of 
reflexion, erect themselves by degrees when the incidence increases, and form with the 
plane of reflexion an angle which becomes larger and larger, until they become per- 
pendicular under the incidence of 90°? Now from the formule of M. Cauchy, the 
reflected ray of which the intensity is perceptibly constant, and increases slowly in 
proportion as the incidence increases, is the ray Ii; therefore it is for this ray that 
