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.

294 UNDULATORY THEORY 0F OPTICS.
and thus there will be an excess of some colours, and the
light will be strongly coloured.
70. There is also another reason. By a small change of
the angle of incidence we produce a small change in y; and
do3 tan 3
as ---
dy tan y
this produces a great change in 3 (B being nearly = 900).
Consequently the change in D cos3 is considerable: and the
expression for the intensity of light will be varied much.
If then the light of the clouds fall in different directions
on this combination of prisms, or if the sun light be made
(by a lens) to fall on it in different directions, the light
both reflected and transmitted will form on a screen bands
of light. As the position and breadth of these bands are
different for every different colour, the mixture forms a very
splendid series of coloured bands, in which the succession of
colours differs from that produced by almost every other
phenomenon of interferences. The same effect may be seen
as well if the combination of prisms be held to the eye: when
the light coming in different directions to the eye will exhibit
the bands in great perfection.
PRoP. 18. Two convex lenses of small curvature, or
a convex lens and plane glass, (fig. 19) are placed in contact: to find the intensity of the light reflected and transmitted at any point M.
71. The two surfaces at M will be so nearly parallel
that we may without sensible error consider them as parallel:'* and therefore the investigations of Prop. 15 and 16
apply. It is only necessary to find an expression for D
* As we shall suppose in the investigation that the separation of the two
surfaces at MI is but a snall multiple of X, it is evident that for the points immediately about i the defect from parallelism will produce an error amounting
only to a very small fraction of X: and therefore the small waves in (32) will
have their effects added together in the direction in which light is reflected from
one of the surfaces, nearly in the same degree as in the direction in which it
is reflected from the other surface.