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.

348 UNDULATORY THEORY OF OPTICS.
angles, they must be combined with the angles in the expres-7r
sion for the vibration. Thus for instance, if a sin (vt- )
were the expression for the vibrations perpendicular to
the plane of incidence on the supposition that they were
not accelerated, a sin {2 (vt - x) + 20 would be the expression on the supposition that they were accelerated.
135. The only thing which concerns us experimentally
is the difference 20-20 (which we shall call ') of the accelerations, for vibrations perpendicular to and parallel to
the plane of incidence. Now
tan (t - ) = cosi /(t2sin2i - 1),asini z
whence cos 1- tan2 (A - 0) 2g2 sin4i - (l + L2) sin2i + 1
whence cos -- =
] + tan~ (( - 0) (1 + tx) sinéi - 1
It appears from this expression that = 0 when sini=-,
or when sini = 1: and that S is greatest when
* 2
sin2 i =
1 +,j
the value of cos being then
8fu2
(i + 2)21
If we assume S= 45~, we have this equation:
2 g2
(1 + g2) cosec"i - cosec4i 2
the solution of which, supposing y = 1,51, gives
i = 48~.7'.30", or 54~,7'.20".
If then light be incident internally on the surface of crown
glass at either of these angles, the phase of the vibrations