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.

REFRACTION OF LIGHT. 269
tlie plane which touches all the spheres, and which evidently
makes the same angle with CA' that A'E or AC makes
with it, but inclined the opposite way. The motion of the
wave, which is perpendicular to this front, makes therefore
the same angle after reflection as before.
It must be remarked that this demonstration is in no wise
affected if we suppose all the spherical waves to be accelerated or retarded by the same quantity. If then we should
find occasion. hereafter to assert that in some cases the direction of vibration is changed at reflection, or (which amounts
to the same) that half the length of a wave must be added
to or subtracted from the path after reflection, the demonstration of the law of reflection will not be invalidated.
PROP. 30. To explain the refraction of light on the
undulatory theory.
33. We must assume that the waves are transmitted
with smaller velocity in glass, water, &c., and in all substances commonly called refracting media, than in what we
call vacuum. This assumption appears in the highest degree
probable, whether we suppose the vibrations in the refracting
media to be vibrations of the same ether, incumbered by its
connexion with the particles of the refracting body, or we
suppose the vibrations to be vibrations of the particles of
the refracting body.
34. Now in fig. 9, let ABC be the front of a wave
going in the direction of AA'. As soon as each successive
small portion of this wave has reached the surface CA' of
the refracting medium, suppose it to cause an agitation in
the ether or the particles of the medium at that surface,
and consider that agitation to be the center of a wave, which
diverges in a spherical form in the medium with a less
velocity than the velocity of the plane wave. Consider the
state of the particles when A has arrived at A'. B has
reached B' some time before: and would have arrived at D
if not interrupted by the refracting medium. Consequently
it has diverged into a sphere ab whose radius is less than