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.

370 UNDULATORY THEORY OF OPTICS.
— 1 - sin(2a+2).sin — },
2 k
or -1-sin 2 \. sin --.
161. Since a does not enter into this expression, the
appearance will not be altered on turning B round its spindle. When sin 2f = o, that is when - =0, or 900, or 180~,
a2
or 270~, the intensity is-: this shews that there is a cross
with light of mean intensity interrupting the rings. When
' is > 0< 90~ or> 1800 <2700, the expression is maximum
when
2 7r1 37r 7 r
=_, -, T &c.
2
and minimum when
7r I r- 5 r
-- =,, &c.
or maximum when
3X 7X
-,I Q -,. &c.
4 4
and minimum wlien
4 4
I= -, &c.
When 'k is > 900 < 180 or > 2700 < 3600, the expression
is maximum when
I -—. —, &e.
4' 4
and minimum when
3s 7X
I=-, -, &c.
4 4
Thus it appears that of the four quadrants into which
the cross divides the image, each opposite pair is similar,
but each adjacent pair is dissimilar: the bright rings in one