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.

LIGHT REFLECTED FROM THIN PLATE. 289
If then the extent of vibration in the light reflected from
C be A sin (vt - ), where the distance x is measured
by the equivalent path in air; then the extent of vibration
in the wave reflected from E will be represented by
B sin 2 (vt - x - 2D cos 3);
x
and the whole intensity will be the intensity of the light in
which the displacement of a particle is represented by the
sum of these quantities. It must be recollected that by
the reasoning in (37) we are entitled to suppose that the
signs of A and B are different.
65. We have here however omitted the consideration
of that part of the light which is reflected from F to H,
again partially reflected at H and partially refracted at K:
and the other parts successively reflected. It is plain that
(putting V for 2Dcos/3) the part refracted at K will be
retarded 2 V: that at the next point 3 V: and so on. Now
suppose that when light goes from glass to air, the incident
vibration being
a sin - (t - x),
the reflected vibration is
9qr
b. a. sin- (v t - ),
and the refracted vibration
2ir
c. a. sin (v t - ):
and suppose that when light goes from air to glass, the
coefficient is multiplied by e for the reflected vibration, and
by f for the refracted vibration. Then if the coefficient for
the light passing in the direction BC is a, that for the
vibration reflected at C will be ab: that for the vibration
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