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.

.344 UNDULATORY THEORY OF OPTICS.
reflected light will consist solely of vibrations perpendicular
to the plane of reflection. The condition i'+ i= 90 gives
sin i
sin i'= cos i, or = cos i, whence tani = u:
which (95) defines the polarizing angle. Thus the angle of
incidence at which, according to theory, the vibrations of the
reflected ray are entirely perpendicular to the plane of incidence, is the same as the angle at which, in experiment, the
reflected ray is entirely polarized in the plane of incidence.
And we have found from theory in (111) that the ray of
a uniaxal crystal which undergoes the ordinary refraction,
and which (94) is said to be polarized in the principal plane,
is produced by vibrations perpendicular to the principal
plane. These are the two reasons which induce us to say,
as in (100), that light polarized in a particular plane consists of vibrations perpendicular to that plane.
131. Another remarkable inference is this. If the two
surfaces of a glass plate are parallel, i and i' at the second
surface are the same as i' and i at the first. Consequently,
if the light reflected from the first surface is polarized, or
if i + i' at the first surface = 90~, i + i' at the second surface
also 90~, and therefore the light reflected internally from
the second surface is also polarized. This is true in experiment.
Many investigations applying to these problems are to be
found in the Cambridge Transactions and other Transactions,
the Philosophical Magazine, and the Comptes Rendus of the
French Academy.
PROP. 27. Light polarized in a plane inclined by the
angle a to the plane of incidence falls on the surface of
a refracting medium: to find the position of the plane of
polarization of the reflected light.
132. The displacement of a particle of ether before
incidence may be represented by
a sin (v t - x)
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