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.

SPECTRA PRODUCED BY REFLECTION FROM STRIATED SURFACES. 317
both distant, then a point G may be found such that the
paths FA4G, FBG, &c. will not sensibly differ in length-;
and therefore the small waves which are produced by the
same great wave, coming from every part of the surface,
will meet in the same phase at G. And this will be true
whether any part of the surface is removed or not. But
at H there will be no illumination, because we may divide
the surface into parts A, a, B, b, &c. such that the path
FaH (supposing the surface a continuous plane) is less
than FAH by -, and therefore the small.wave coming from
a will destroy that coming from A; the small wave coning from b will destroy that coming from B: and so on.
Now suppose that we remove the parts a, b, c, d, &c. There
is now no wave to destroy any one of those coming from
A, B, &c.: and they will not destroy each other, because
the path FBH being less than FAH by X, FCH being
less than FBH by X, &c., they are all in the same phase.
Consequently there will be brightness at H. For different
values of X it is evident that we must take points at different distances from G: and thus spectra will be formed
nearly as in (84).
For calculations applying to various cases of interference,
the reader is referred to several volumes of the Cambridge
Transactions, and of the Philosophical Magazine.
APPLICATION OF THE THEORY OF UNDULATIONS TO THE
PHENOMENA OF POLARISED LIGHT.
89. In the preceding investigations no reference has
been made to the direction in which the particles of the
luminiferous ether vibrate. They might, like the particles
of air in the transmission of sound, vibrate in the direction in which the wave is passing: or they might, like the
particles of a musical string, vibrate perpendicularly to the
direction of the wave, but all in one plane passing through
that direction. To these or any other conceivable vibrations
our investigations would apply equally well: ail that is required being that they should be subject to the general law