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.

CHARACTERISTICS OF AN UNDULATION. 241
3. As another example, let (/3), (y), (S), (e), (j), of
fig. 2, represent successive states of the particles which when
at rest were in the position (a). If we fix our attention
on one of the most elevated parts, as for instance k, at T,
we find that at T + - the elevation has passed to a'; at
4
2r
T + -to d': &c.: though tle particles have had no motion
whatever in that direction. And if these motions were actually before us, we should see several elevations passing
uniformly and continuously from the left to the right. But
if we fixed our attention on any one particle, we should see
that it has an oscillating motion above and below the line.
The particle a for instance, is at its greatest elevation at
~T 37
+ -, and at its greatest depression at T +-: d is at
its greatest depression at T, at its greatest elevation at
2T
T+ -, and at its greatest depression at T + 7: and so
4,
for the others. This varying state of particles is therefore
another instance of undulation, the motion of every particle
being at right angles to the direction of transmission of the
wave.^v
We might conceive more complicated cases of undulation,
as when the motion of the particles is compounded of the
two motions supposed in these two cases; or when there is
one motion similar to that represented in fig. 2 in the plane
of the paper, and another perpendicular to that plane, &c.
The last of these suppositions is that to which we shall hereafter refer the phenomena of polarization, and of Optics in
general.
PItoP. 2. The length of a wave does not depend on the
extent of vibration of each particle.
4. It is easily seen that the interval between corresponding points of two waves of condensation in fig. 1 (which is
This is nearly the kind of undulation which takes place on the surface of
deep water in a calm.
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