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.

TOTAL INTERNAL REFLECTION OF POLARIZED LIGHT. 349
in the plane of incidence is accelerated more than that of
the vibrations perpendicular to the plane of incidence by 45~.
If the light be twice reflected in the same circumstances and
with the same plane of reflection, the phase of vibrations in
the plane of incidence is more accelerated than that of the
other vibrations by 900.
136. If then we construct a rhomb of glass, fig. 33,
two of whose sides are parallel to the plane of the paper,
and the others perpendicular to the paper and projected in
the lines AB, BC, CD, DA; and if the angles at A and C
are 540.37': then light incident perpendicular to the end at
F will be internally reflected at G and I, making at those
points angles of incidence 54~.37', and will emerge at I in
the direction parallel to that in which it entered at F. The
immersion at F and the emersion at I will produce no alteration in the light, but the effect of the two reflections at
G and H will be to accelerate the phases of vibration in
the plane of the paper more than those perpendicular to
that plane by 90~. A rhomb thus constructed we shall call
Fresnel's rhomb.
PROP. 29. Polarized light is internally reflected in a
refracting medium at an angle of incidence greater than that
necessary for total reflectidii: to find the nature of the reflected ray.
137. Let thé plane of polarization make with the
plane of incidence the angle a. Then the vibration, represented by
a. sin (vt - V),
is performed in a direction making the angle 90 - a with
the plane of incidence. Consequently the resolved vibrations are
a. cos a. sin - (vt - w)