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.

240 UNDULATORY THEORY OF OPTICS.
about d' are closer together than they were. At the time
2T
T + - the point of greatest condensation has advanced to
g', precisely the point where at the time T there was the
least condensation: at the time T +, it has advanced to
4
k': and at the time T + T, to a". The particles are now,
it may be observed, in just the same state as at the time T,
for a" was then the center of a condensed group. After this,
every thing goes on in the same manner, beginning at the
time T + T, as it did beginning at the time T. All that
we have said with respect to the condensed mass about a'
applies to those about a, a", and a"'. Now if these motions
were really going on before our eyes, we should see several
condensations (not the condensed particles) passing uniformly
and continuously from the left to the right of the line of
particles.
But if we fix our attention on any one of these particles,
we shall see that it has a reciprocating or oscillating motion.
The particle a is advancing froin T to T +- when it has
4
attained its greatest advance: it recedes then to T+ (: it
then advances again. The particle d advances from T (when
2r
it is at its minimum advance) to T + -: it then recedes
4
to T +. The particle g recedes to T+ - then advances
to T +, then recedes. And so for the others. The varying state of particles which we have here supposed, satisfies
therefore the conditions mentioned in (1), and therefore this
is an instance of undulation, the motion of every particle
being backwards and forwards in the same line as the direction of transmission of the wave*.
This is the kind of undulation which in the air produces sound, and is the
only kind which, till within a few years, was used for the explanation of the
phenomena of Optics.