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.

288 UNDULATORY XIHEORY OF OPTICS.
that light moves more slowly in glass than in air. The
whole of the investigation of the last proposition depends
on this assumption.
PaoP. 15. A series of waves is incident upon two
plates of glass separated by a very small interval (fig. 17);
part of the light is reflected at the lower surface of the
first glass and part at the upper surface of the second
glass: and these portions interfere: to find the intensity of
the mixture.
64. Let AB be the path of one portion which is refracted in the direction BC, and of which one part is reflected in the direction CD, while another part is refracted
at C and falls on the second plate at E, is partially reflected to F, and partially refracted in the direction FG
parallel to CD. Draw FD perpendicular to CD. Then
the path which one wave has described in going from C to
D, measured by the equivalent path in vacuum, is tx. CD:
while that which the other has described in going from C
to F (where its front has the same position as the front of
that which has reached D) is CE+ EF. The excess of
the latter above the former is
CE + EF - Mu. CD.
Let D be the distance of the plates, y tle angle of incidence at C, 3 the angle of refraction. Then
2D
CE +EF =
cos /
and CD = FC. sin = f2D. tan f. sin y;
sin f
also ux =:
sin y
therefore the excess
2D 2D.sin'/3 D
cos== — 7 ~ — 3T =2 D cos s.
cos P cos P