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.

RINGS WITH CIRCULARLY-POLARIZED LIGHT. 37I
quadrant having the same radii as tle dark rings in the
next quadrant. And on comparing these expressions with
those in (157), it will be seen that the effect of placing
Fresnel's rhomb has been to push the rings outward by {
of an order in two opposite quadrants, and to pull them in
by 1 of an order in the other two opposite quadrants. At
the same time the cross which was perfectly black has now
some light. The most important difference of character
however which the use of Fresnel's rhomb produces is the
unchangeability of appearances as B is turned round.
If we compared the rings produced with the same position of Fresnel's rhomb by two crystals, in one of which c2
was >a2 and in the other of which c2 was <a2, then for
a given order of rings, that is for those in which the magnitude of 0, without respect to its sign, is the same, sin -
would be positive for the first and negative for the second,
or vice versa. Consequently the bright rings of one crystal
would correspond to the dark ones of the other. But we
have seen that the bright rings of one quadrant correspond
to the dark rings of the neighbouring quadrant. Consequently the rings presented by one of the crystals would
be the same as those presented by the other, supposing the
latter rings turned round 90~. This affords a convenient method of determining whether the double refraction of a given
uniaxal crystal is of the same kind as that of a standard
crystal (for instance Iceland spar) or of the opposite kind.
PILOP. 34. A plate of a biaxal crystal whose optic axes
make a small angle with each other (as nitre or arragonite)
is bounded by planes perpendicular to the plane passing
through the axes and nearly perpendicular to each axis;
light is incident at a small angle of incidence: to find the
difference of retardation of the two rays.
162. The accurate solution of this problem leads to
some rather complicated expressions: and we shall therefore
content ourselves with a very approximate solution analogous
to that found in Prop. 31. We have found there that the
difference of retardation was nearly
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