Mathematical tracts on the lunar and planetary theories, the figure of the earth, precession and nutation, the calculus of variations, and the undulatory theory of optics.

REFLECTION FROM METALS. 3 5
reflection from metallic surfaces is not strictly analogous to
the reflection of sound from a wall, but has a closer relation
to reflection from a surface terminating a dense medium*.
Whether any explanation could be founded on the supposition that the ether is absolutely terminated at the reflecting surface, or that the ether within the metal is in a
rarer state than that external to it, is a point that has
not been examined.
ON THE COLOURED RINGS PRODUCED BY INTERPOSING A
CRYSTALLINE BODY BETWEEN A POLARIZING PLATE
AND AN ANALYZING PLATE.
144. In (97) we have mentioned as one of the fundamental facts of polarization that if the planes of reflection
of A and B in fig. 24 are at right angles to each other, the
angles of incidence at both being the polarizing angles, the
* It appears from Sir David Brewster's experiments that, in reflection from
metals, the proportion of the vibrations parallel to the plane of reflection in the
reflected ray to those in the incident ray, is less than the proportion of the
vibrations perpendicular to the plane of reflection in the reflected ray to those
in the incident ray. Consequently, after a great number of reflections from
metallic surfaces, the reflections being all performed in the same plane, the
vibrations parallel to that plane are diminished in a rapidly decreasing geometrical series, and are soon insensible, and therefore the light appears to be
polarized in the plane of reflection. This happens with a much smaller number
of reflections from steel than from silver. It appears also that the alteration of
phases of the two sets of vibrations is somewhat different for different metals,
and different at different angles of incidence; beginning to be sensible at the
incidence 40~ nearly, and amounting at its maximum (which it has at an incidence of nearly 70~) to about 90~: perhaps to more, but Sir D. Brewster's statements leave it doubtful. It is also doubtful whether the phase of the vibrations
parallel to the plane of incidence is accelerated or retarded. See Brewster on
Elliptic Polarization, Phil. Trans. 1830. The nature of elliptically polarized light
had been sufficiently indicated in a few words by Fresnel, and the merit of this
valuable paper consists entirely in shewing that the reflection of polarized light
at a metallic surface produces light of that kind. The result of these laws, on the
principles of the text, may be thus stated. If the incident vibration perpendicular
to the plane of incidence is a. sin (vt - x + A); the multiplier of the coefficient
in the reflected ray p: the corresponding quantities for the other vibration
b.sin(vt - x + B) and q: and the acceleration of the latter ô: then after n reflections the vibration perpendicular to the plane of incidence is
a.p'. sin (v t- xv + A),
and that parallel to the plane of incidence
b.q. sin (v t - + B + no).
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