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.

REFLECTION ACCOMPANYING REFRACTION. 271
can be found which touches all the spheres. There will be
no grand wave. therefore: and the little waves causing displacements in different directions will very soon destroy each
other. Thus there will be no refracted ray. This is a well
known law of optics.
It must be remarked that the demonstrations of (32)
and (34) are not free from obscurity, for the reason mentioned in (22).
36. There is another phenomenon attendant on refraction which we can explain but vaguely, though it is easily
seen that the explanation is not without foundation. The
particles of ether next in contact with the glass, (if we
suppose glass to be the refracting medium) communicating
motion to the denser ether within the glass, may be considered as small bodies striking large ones. Now if they
followed the same law as elastic bodies*, a certain motion
would be communicated to the large bodies, and the sinall
bodies would lose their original motion and would receive a
motion in the opposite direction. The motion of the struck
bodies causes the refracted wave of which we have just
spoken; the motion remaining to the striking bodies will
cause a reflected wave in the ether. The magnitude of the
reflection will plainly be diminished as the difference between
the particles is diminished. Thus refraction is always accompanied by reflection: and the reflection is more feeble as
the vibrating media on both sides of the surface approach
more nearly to the same state: that is, as the refractive
index approaches to 1. This is experimentally true.
37. If, however, the rays are passing from glass to air,
we must represent the state of the particles by large bodies
striking small ones. The small bodies receive a motion,
which causes the refracted wave: the large bodies will preserve a part of their motion in the same direction, and this
* The motions would follow this law, if the particles acted on one another
like those of air by condensation or rarefaction of the fluid between them: or in
the manner which Fresnel supposes (to be alluded to hereafter): or in any way
which makes the force equal at equal distances of the particles. We are not
therefore making the forced supposition of particles impinging on each other.