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.

318 tJNDULATORY TtEORY 0O OPTICS.
of undulations, and that for a considerable number of vibrations the extent and time of vibration should be the same.
The phenomena of polarization however enable us to point
out what is the kind of vibration.
90. The properties of Iceland spar (which, it has since
been discovered, are possessed by the greater number of
transparent crystals) first pointed out the characteristic law
of polarization. If a pencil of common light be made to
pass through a rhombohedron of this crystal, it is separated
into two of equal intensity. This may be shewn either by
viewing a small object through it, when two images will be
seen; or by placing it behind a lens on which the light of
the Sun or that of a lamp is thrown, when two images
will be formed at the focus. A line drawn through those
two images is in the direction of the shorter diagonal of
the rhombic face of the crystal; the rhombohedron being
supposed to be bounded by planes of cleavage, and the
pencil of light being incident perpendicular to one of them.
91. On examining the paths of these pencils within
the crystal, it is found that one of them obeys the ordinary
laws of refraction, but the other follows a more compli'cated law (which we shall hereafter describe). The first
is therefore called the Ordinary pencil, and the other the
Extraordinary pencil: and they are frequently denoted by
the letters O and E.
92. To the eye no difference is discoverable between
the two pencils, or between either of them and a pencil of
common light whose intensity is the sanie. Yet the properties of the light in the two pencils are different, and both
are different from common light. For if we take one of
the pencils (for instance O) and place a second rhombohedron before it; on turning the first rhombohedron it is
found that in general the second crystal separates the pencil
O into two of unequal intensity, one following the ordinary
law and the other the extraordinary law (which we may
call Oo and Oe), and that in certain relative positions ot
the crystal one of the pencils wholly disappears. On ex