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.

INTERFERENCE PRODUCED BY A PRISM. 283
by several lengths of waves. In general, when white light
is used, no bars can be seen where the length of one path
exceeds that of the other by ten or twelve times the mean
value of X.
53. The quantity X, as we have mentioned in (23), is
so small that it could not be made sensible to the eye. But
sin a may be made as small as we please, and consequently
+ b X may be made large enough to be easily visible to
a sin a
the eye. It is by this and similar means that the lengths
of waves for differently coloured light have been measured.
54. The agreement of the facts of experiment with these
conclusions from the theory is most complete. And this
may be considered as the fundamental experiment on which
the undulatory theory is established. It is perfectly certain
in this experiment that the mixture of two streams of light
whether white or coloured does produce black. The bars
next the central white are remarkably black: and the dark
bars beyond the next bright bars are also very black: and
upon intercepting either stream of light all these dark bars
become bright. It appears plain that no theory of emission
of particles can explain this fact: and it seems difficult to
conceive that any theory except that of undulations can explain it.
55. We shall occasionally have to mention the system
of bright and dark bars described in (52). We shall generally call them the fringes of interference.
56. The reader is particularly requested to observe that
when a + b or the distance of G and H from the screen is
given, the breadth of the bars for any given colour is inversely as a. sin a (48), or inversely as GH. And generally,
the nearer together are the two sources of waves which interfere, the broader are the fringes of interference.
PROP. 13. A series of waves diverging from a point A
fig. 15, falls upon the prism BCD, each of whose sides BC,