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.

282 UNDULATORY THEORY OF OPTICS.
4 /c2 r X'
for the intensity of the next kind of light, 4 cos
(a + b)2 X"
4c'" 7rX
for the intensity of the third kind of light, (a + bcos -"''
(Ca + b li
and so on. If they liad been in the same proportion as
in the light reflected from a single mirror, the intensities
would have been
4 c' 4c"42 4c'2
(a+b)2 (a+ b)2' (a+b)2'
The different colours therefore are not mixed in the same
proportion as in the original light. The same may be
shewn of any other point: and thus if the original light
be white, no point of the screen will be illuminated with
white light except the middle of the central bright bar.
52. The same thing may be thus shewn. The breadth
of the bright and dark bars for each colour is proportional
to the value of X for that colour (48). Consequently the
bars are narrower for the blue rays than for the green:
narrower for the green than for the yellow; &c. by (23).
The line passing through the paper at O is however to be
the center of a bright bar of each colour. In that line therefore there will be a perfect mixture of all the colours at
a line on each side there will be nearly a total absence of
all: but beyond this the red bars will sensibly overshoot
the yellow and green and blue bars, and the more as we
recede farther from the center. Consequently the bars will
be coloured, the bright bars being red on the outside and
blue on the inside. And after two or three bars, the outside of the red bars will mingle with the inside of the next
blue bars, and there will be no such thing as a black bar.
This will continue as we recede from O till the colours become mixed in such a way that it is impossible to distinguish
the bars, and the whole is a mass of tolerably uniform white
light. This indistinctness of bars, and ultimately their disappearance, always take place when one of the mixed strearns
of light has described a path longer than that of the other