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.

296 UNDULATORY THEORY OF OPTICS.
(2) The most brilliant light is reflected when
X sc X3X s ec 5X sec
OM2 =.., or= - -, or=, &c.
2 l-+ 2 (-+-) 2 - +-)
\r r r I r r
Consequently between the dark rings there are
bright rings, the squares of the diamneters of whose
most brilliant parts are in the proportion of
1 3 5
&c.
- 5 95 9 C.
2' 2' 2'
(3) The diameters of these rings are coeteris paribus
as \/(sec /3). Consequently on inclining the incident ray, or on depressing the position of the eye
by which they are viewed, the diameters of the
rings increase.
(4) For differently coloured rays, the diameters of the
rings vary as x/(X). The different colours which
are mixed in white light produce therefore a series
of rings whose diameters are different, and which
overlapping each other produce a series of colours
analogous to those mentioned in (52). The colours
at last become mixed to such a degree that no
traces of rings are visible.
(5) The diameters of the rings vary, ceteris paribus, as
1
\/ (r r i
To inake the rings large, therefore, - + - must be
r r
small, or r and r' must be large. If the lower
glass be plane, or -,=, the diameters of the rings
vary as \/(r).