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.

272 UNDULATORY THEORY OF OPTICS.
will cause a reflected wave. Thus when light passes through
glass there will be reflection at both surfaces. But there is
this difference between the two reflections: one is caused by
a vibration in the same direction as that of the incident ray,
and the other by a vibration in the direction opposite to
that of the incident ray. We shall find this distinction important in explaining a fundamental experiment (65).
The same thing may be thus shewn. If we suppose a
mass of glass to be cracked and the separated parts to be
again pressed close together, there will be no more reflection
than from the interior of a mass of glass: that is, there will
be none at all. Still as there are really two surfaces in contact, each of which separately reflects, we must suppose the
reflections to be of such a kind that they destroy each other.
Consequently if the vibration from one reflection be in one
direction, that from the other reflection must be in the opposite direction.
38. We shall now state a difficulty in the undulatory
theory of refraction which has not yet been entirely surmounted, but which does not appear by any means insurmountable. The index of refraction we have found to be
the proportion of the velocities of the waves in vacuum and
in the refracting medium. Now it is well known that, experimentally, the refractive index is different for rays of
different colours, that is, for waves whose lengths are different.
It is evident then that waves whose lengths are different are
transmitted with different velocities either in vacuum*, or
in the refracting medium, or in both. The difference does
not depend on the extent of vibration of each particle, for
the refractive index is the same for a bright light as for a
feeble one, but merely on the length of the wave, or on the
time of vibrationt. We are unable to explain this; and the
* If the velocities for different rays were different in vacuum, the aberration
of stars (which is inversely as the velocity) would be different for different
colours, and every star would appear as a spectrum whose length would be parallel to the direction of the Earth's motion. We know of no reason to think
that this is true.
t The difficulty might perhaps be explained thus. We have every reason to
think that a part of the velocity of sound depends on the circumstance that the