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.

284 UNDULATORY THEORY OF OPTICS.
CD, makes the small angle a with the third side: to find
the intensity of illumination on different parts of the screen
EF where the two streams are mixed.
57. The investigation is exactly similar to that of the
last proposition, with this difference only. By common Optics,
AG = AH= CA. (ut - 1). sin a nearly, = (u - 1). a sin a nearly.
In the former investigation we had GL = LH = a sin a. Consequently where we find a sin a in the former investigation
we may put (u - 1). a. sin a, and we shall have the correct
expression for this case. Thus the intensity of illumination
4 2 27r ( - 1)a sin a
---- COS o0
(a + b)2' X a+b
and the interval at which the centers of the bright and
black bars succeed each other is
a +b X
(ut - 1) a sin a' 4
58. The results are exactly similar to those obtained
in (50), (51), (52), (the absolute breadth of tle bars being
different) with the following exception. The breadth of
the bars for different colours does not (as before) depend
simply on X, but on. Now g varies with X: it is
-L-1
greatest for the blue rays or those for which X is least,
and less for those for which X is greater, through all the
different colours. Consequently the breadths of the bars
formed by the different colours are not in the same proportion as before, but are more unequal. The mixture of
colours therefore at the edges of those bars which are a
little removed from the central bar is not the same as
before; and after a smaller number from the center, the
colours of the different bars are mixed with each other (52).
PROP. 14. Suppose that in the experiment of Prop. 12
or 13 a thin piece of glass PQ is placed in the path of one