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.

SEPARATION OF COLOURS BY BIAXAL CRYSTALS. 377
curves are ceteris paribus larger for red than for blue
rays.
169. There is however one difference between the curves
for the different colours which in its nature is unlike any
thing else that we have yet seen. It is that the optic axes
for different colours do not coincide. In every instance however the alteration of, place is symmetrical with regard to
the two axes. Thus the red axes may make with each
other a smaller angle than the blue axes, or vice versâ,
but the angle between one red and one blue axis is the
same as that between the other red and the other blue.
In one or two instances this amounts to nearlv 10~. The
consequence is that the colours are not the same in different
parts of the rings of the same order. Suppose for instance
(as in nitre) the red axes are less inclined than the blue.
As the red rings are larger than the blue, we shall on
taking points exterior to A and B find positions where all
the colours are mixed or all are absent, and therefore the
rings are nearly white and black. If we trace the same
rings to the positions between A and B, the red rings will
very much over-shoot the blue rings, and therefore the
rings have the colour peculiar perhaps to a high order in
Newton's scale.
170. It was till very lately supposed that the axes of
the different colours were all in the same plane. Sir J. Herschel has discovered that in soine instances (in borax for
example) this is not true: the planes, however, as far as yet
observed, all pass through the line bisecting the angle formed
by the two axes. The reader will have little difficulty in
conjecturing the nature of the alteration which this irregularity produces in the colour of the curves.
PROP. 36. In the experiment of Prop. 35, Fresnel's rhomb
is interposed between the polarizing plate and the crystal:
to find the form, &c. of the coloured curves.
171. As in (160), the intensity of light at any point is
- Ê1 - sin (2q + 2 a). sin X —