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.

380 UNDULATORY THEORY OF OPTICS.
(3) Colours may also be produced by applying together,
with their axes parallel, two plates cut from uniaxal
crystals, one of the positive and one of the negative
class (as quartz and beryl). For in one of these
the Ordinary ray is most retarded, and in the other
the Extraordinary ray is most retarded: and as the
Ordinary ray in one forms the Ordinary ray in the
other, the ray which is most retarded in the first
is least retarded in the second, and thus the difference of retardations may be made as small as
we please.
(4) From the bodies which crystallize in laminoe it is
frequently possible to detach a plate so thin that
it will exhibit colours: for instance sulphate of lime,
or mica. Both these are biaxal: in the former the
axes are in the plane of the laminoe: in the latter
they are in a plane perpendicular to it, but widely
separated.
(5) In all these cases, the colours do not form small
rings, as in the cases that we have treated at length,
but are diffused in broad sheets. This arises merely
from the circumstance that the expression for I
or I - I varies very slowly with the variation of
incidence. In sulphate of lime, for instance, a ray
perpendicular to the laminae makes
m = 90~, n = 90':
a ray inclined to this will produce very little alteration in sin m'. sin n' on which I depends. The same
is true in mica, where the ray makes equal angles
with the two axes. If it be inclined in the plane
of the axes, sinm'. sin n' is diminished: if perpendicular to that plane, it will be increased.
173. If the thickness of a lamina of sulphate of lime
or mica is such that, for a ray perpendicular to the lamina,
I=- for mean rays, the lamina may be used instead of
4
Fresnel's rhomb. For here the light which is incident is