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.

384 UNDULATORY THEORY OF OPTICS,
bending it by a weight or a screw pressing the middle,
and in that state placing it edgeways between the polarizing
and analyzing plates at an angle of 450 to each plane of reflection. A black line is seen along the middle extending
the whole length, with stripes more and more coloured on
each side: the number of stripes is greatest in the middle
of the length (perhaps six dark and as many bright): towards the ends the stripes become broader and fewer, and
the ends are wholly black. It is plain here that the central black line is seen in those parts which suffer no strain;
and that those which are extended as well as those which
are compressed possess double refraction. On putting a
plate of mica across it, with the plane of its axes either
parallel or perpendicular to the plane of the glass, and
comparing its effects on the fringes with its effects on the
rings of Iceland spar &c., it is found that the double refraction of the compressed parts is of the same kind as
that of a negative crystal, and that of the extended parts
of the same kind as that of a positive crystal, the axis
being supposed to lie in the direction of the length of the
glass plate.
179. It is found also that if glass is heated in one
part, or if it is heated generally and cooled in one part,
or if it is made nearly red hot and suddenly cooled by
placing between cold irons &c., it possesses the property of
exhibiting beautiful colours divided by black brushes &c.,
when placed between the polarizing and analyzing plates.
There is no doubt that the glass is here in a state of
mechanical constraint. On turning the glass, the black
brushes are seen to pass by turns over every part. This
determines the plane of polarization of the rays at every
part of the glass, since at that point (172) ô must = 0,
90~, &c.: that is, the two planes of polarization are then
parallel and perpendicular to the plane of first polarization.
180. Between constrained glass and crystals there is
however one important difference. The rings &c. exhibited
by crystals respect a direction which is independent of the
size of the specimen or the part from which it is taken.
The smallest fragment of crystal properly shaped may be