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.

290 tNDULATORY THEORY OF OPTICS.
refracted at F, acef: that for the vibration refracted at K,
ace3f: and so on. Thus the whole vibration is
ab sin-(vt -,) + acef{sin-(vt - - V)
27 2
+ e sin - (v t - - 2 V) + e4 sin (vt - x - 3 V) + &c.
f. 2n nsin (vt-(- V)-esin (vt-cx)
x) (vt-)+ cef 2 kt À J
I - 2e2cos - V+ e4
We shall anticipate so much of succeeding investigations
(see Art. 125 and 126) as to state that, whether the vibrations are in or perpendicular to the plane of incidence*,
there is reason to think that
e
== - 1, and cf= -e2.
Using these equations to simplify the expression; resolving
it into the formn
Fsin (v t - ) + G cos - (vt - )
3. \
as in (17); and, as in (17) and (23), taking F2 + G2 to
represent the intensity, we find for the brightness of the
reflected light
4a e sin2 rV 4a2 e"sin" D cos/3
or.gw'1 - 2 e2co — ( e)24ein cos+ (-e + sin cos
À À
66. The supposition that we have made is that of a
thin plate of air or vacuum inclosed between plates of
glass, or mica, &c. But it is plain that the investigations
* When there are vibrations of both these kinds, it is necessary to calculate
the illumination from each, and to take their sum.