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.

FRINGES SHIFTED BY INCLINING AN INTERPOSED GLASS. 287
or Mi.ST in air. Consequently the retardation (measured by
the space, which the wave would have advanced further, if
it had moved in air) is. ST - Ss.
And the retardation of the portion incident at X is
(y - 1) XY or (/ - 1) T'.
Therefore the upper pencil is more retarded than the lower by,.ST- Ss- (-) T'.
The angle of incidence is f3: and if y be the angle of
refraction,
ST T' d T'.cosG-y)
S, and SS.cos
cos y cos y
sin 3
also u =-;
sin?
the retardation =
T sin3 cos ( - ) sin/3 +]
sin 7 cosy cos 7 sin 7
= 2 ' (sin2 -. sinm2.
If 3 be small,
7 1. 3
sin -. in very nearly,
and the retardation
= 2 T(' - -1 ) sina2 nearly.
This is to be substituted for ( - 1)T in the expressions
of (59) and (60).
63. These conclusions are fully supported by experinient: and this is important as establishing one of the fundamental points of the undulatory theory of Optics, namely