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 TRANSMITTED THROUGH THIN PLATE. 291
apply in every respect to a thin plate of fluid with air on
both sides: as for instance a soap-bubble. To examine
particular cases,
(1) If D= 0, the intensity = 0 whatever be the value
of X. Thus it is found that where plates of
glass &c., are absolutely in contact or very nearly
so, there is no reflection: and when a soap-bubble
has arrived at its thinnest state, just before bursting, the upper part appears perfectly black.
(2) The intensity is also o if
D cos / = -, &c.
But when light of different colours is mixed, it
will be impossible to make the light of all the different colours vanish with the same value of D,
and thus no value of D will produce perfect
blackness.
(3) If D cos = -, and if we take the value of X
corresponding to the mean rays (as the greenyellow), the intensity of light in the different colours
will be nearly in the same proportion as in the
incident light, or the reflected light will be nearly
white. But this will not take place on increasing
the value of D, or the reflected light will be coloured till D is become so large that for a great
number of different kinds of light, corresponding
to very small differences of X, Dos has the
values of successive odd numbers.
Pnor. 16. In the circumstances of the last proposition,
to find the intensity of the light refracted into the second
plate.
67. It is readily seen that the coefficient of the vibration
refracted at E is a.cf: that of the vibration refracted at H
19- 2