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.

366 UNDULATORY THEORY OF OPTICS,
not the same as those of Newton's scale. To such an exav
tent, and so differently in different crystals, does a
vary with X, that in one variety of the uniaxal apoplyllite
avX
Sir John Herschel found that c'- 2 was almost exactly
constant, so that more than 35 rings were visible: while in
another variety c2 - a2 was positive for the rays froi one
end of the spectrum and negative for those from the other
end, and = 0 for the intermediate rays, and only one or two
rings were visible.
158. Let a = 00, or the plane of reflection at the
analyzing plate coincide with that at the polarizing plate.
The expression for the intensity is
a 1 - sin'2 2 sr. sin2_)
This expression, added to that discussed in (157),, produces
a sum a. Consequently the intensity at any point of the
image in this case is complementary to that in the case of
(157). Thus, instead of a black cross interrupting the rings,
there is a bright cross interrupting the rings: instead of
the dark rings having radii
/ 2avX 4avX &
(c' -a )T' (C - a')T
and the bright rings having the radii
/ avX / 3avX
(c - )T' (c- -,)T' &c.
the bright rings have the former and the dark ones the
latter.
159. In the general case, there is no variation of the
intensity with different values of I or i, (that is, there is a
brush of some sort with light of uniform intensity throughout, interrupting the rings), when
sin (2,\/ - 2a). sin 2\ = 0.