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.

COLOURED FRINGES OF INTERFERENCE. 281
considering the screen as extended in the direction perpendicular to the paper, and observing that the investigation
which applies to M applies to every point in the line perpendicular to the paper at M, it is easily seen that the
appearance on the screen is a series of bars alternately
bright and black.
49. We have supposed the plane of reflection to be
perpendicular to the edge wliere the two mirrors touch. If
however it had been inclined in any manner, the result
would have been precisely the same.
50. We have not yet considered the effect of a mixture of light of different colours in the same pencil (such
as exists in white sun-light, and in most kinds of artificial
light). According to the suppositions made in (23) this
is represented by supposing the light to consist of different
series of waves which may or may not be intermixed, the
value of X being different for each different series: and by
(19) these different series cannot affect one another, and
therefore the effect of each in producing illumination of its
peculiar colour is to be considered separately, and the sum
of the effects of all the illuminations to be taken afterwards.
51. Now if we examine the expression for the illumi4~S
nation, it will appear that at O the intensity is -4h
(a + b)2
whatever be the value of X. Consequently, that point is
illuminated by each of the differently coloured lights, with
four times the quantity of illumination which there would
have been if the light from one mirror only had fallen
upon it. But there is no other point in similar circumstances. For if we put X', X", X"', &c. for the lengths of
waves of differently coloured lights, X' being the smallest
and corresponding to the blue light, and ', c", c"' &c. for
the coefficient of displacemcnt, and if we consider the point
a+b X'
where OM=.-, we find
a sin a 2
for the intensity of the blue light, (a - )