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.

INTENSITY OF LIGHT REFLECTED FROM GLASS. 341
densities is 1: 2, or sin i': sin2i. Combining these proportions, the proportion of the masses is
sin z. cos i: sin i. cos i.
Now if an elastic body impinges on an equal elastic body,
it loses its own velocity and communicates to the other a
velocity equal to its own: this is similar to the action of
one mass of the ether in vacuum on the next. Supposing
the similarity of action to apply to the different states of
ether at the confines of the medium, we must compare this
with the motion of two unequal elastic bodies A and B
after the impact of A with the velocity V on B originally
at rest. It is known that A retains the velocity y V,
*' A + B
A+B
and that B receives the velocity 2_ V.. Substituting for
A + B
A, sin i'. cos i, and for B, sin i. cos i', we find for the motion
retained by the external ether, si(i' ) x its previous mosin (i' + i)
2 sin i'cosi
tion; and for that communicated to the internal ether,. si
sin (i' + i)
x previous motion of external ether. Now by a succession
of numerous impulses of this kind, following a given law,
a series of waves with any law of displacement may be produced: and every impulse produces parts in the two media
having the proportions given above. If then the original
displacement be represented by
a. sin (vt - ),
that retained by the external ether, and which produces the
reflected ray, must be
sin (i' - i) 2. 2
a....sin (v t - x),
sin (i' + i) X
and that transmitted to the internal ether, and which produces the refracted ray, must be
2 sin i'.cosi 27r
a. sn- (vt -)m).
sin (i' + i) X