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.

840 UNDULATORY THEORY OF OPTICS.
making them more complete. It is however consolatory to
know that they are fully supported by experiment, and that
they have given a law to phenomena, of which some appeared inexplicable, and others would never have been reduced to laws by observation alone.
127. Suppose that the particles of ether, retaining the
same attractive force*, are in the inside of glass &c. loaded
with some matter which increases their inertia in the ratio
of 1: n, without increasing their attraction. The equation
of (103) would be changed to this:
d'~ u 1 / 1\ m d9u
--- 1-.-.
h dx2
If the solution before were u = ( (vt -.), the solution would
now be
= p (vt - x'n).
The velocity of transmission is diminished therefore in the
ratio of /(n): 1. But we have supposed that the velocity is diminished in the ratio of Mj: 1. Consequently n = '2.
128. Now suppose that we have a series of equal quantities of the ether in a line, and that a transverse motion
is given to the first, which, from the constitution described
in (103), it has the power of transmitting to the second, &c.
When we arrive at the surface of the glass, we must take
volumes of the denser ether, whose dimensions are determined in the direction of the transmission of the wave by
lengths proportional to the velocity of transmission, and in
the other directions by their correspondence with the quantity of ether which puts then in motion. Thus in fig. 32,
BD
if DF= -, the ether in ABDC may be considered as
putting CDFE in motion. Put i for the angle of incidence,
i' for that of iefraction. The proportion of the lengths in
the direction of the ray is u: 1, or sin i: sini'. The proportion of the breadths is cosi: cosi'. The proportion of
Perhaps this supposition is hardly reconcileabld with tliat madg in the last
propositions.