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.

EFFECTS OF CRYSTAL AND ANALYZING PLATE. 38 5
niade to exhibit the rings as well as the largest. In constrained glass, on the contrary, the rings and brushes cannot
be seen, except the specimen is placed so far from the eye
that the whole can be seen at once: and then we perceive
an effect, not similar to that produced by rays passing in
different directions through the saine crystal, but to that
produced by a number of crystals of different doubly-refractive power arranged in different positions and then united
into one system.
181. It may be usefu] to examine the effects of the
three agents which are necessary, and in a particular order,
for the exhibition of these appearances: namely the polarizing plate, the analyzing plate, and the interposed crystal.
We shall begin with the last.
It is necessary that there should be an interposed body
for the purpose of altering the nature of the ray in order
to make it reflexible at the analyzing plate. We know of
only two ways in which this can be done. One is, by resolving the vibrations into two parts and suppressing one
of them. This is done if a plate of tourmaline with its
axis inclined 450 to both planes of reflexion is interposed;
light is then reflected from the analyzing plate. The other
is, by resolving the vibrations into two parts and retarding
one; the retardation being either constant (measured by
its effect on the phases), or varying with the colour of the
light and with the direction of the ray. The first of these
is done when Fresnel's rhomb is interposed: the second
when a crystal or any body possessing double refraction is
interposed. In either of these cases, the nature of the
light compounded of these two parts as they emerge is different from that of the light which enters. When the
planes of reflection at the polarizing and analyzing plate
coincide, the same contrivance is necessary in order to
make the light less capable or wholly incapable of reflexion
at the analyzing plate.
It is necessary for the exhibition of coloured rings that
there should be an analyzing plate, because, in all the cases
of resolution that we know, the intensity of the light pro25