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.

SPECTRA PRODUCED BY GcATING BEFORE A LENS. 315
at the sides there will be spectra similar to those formed
by a prism, their blue ends being nearest to the center.
And as each bright point is almost perfectly insulated, the
spectrum will be pure; that is, there will be no sensible
mixture of colours in any part of it. This is verified completely by experiment: the spectra are so pure that, when
the solar light is used, the fixed lines or interruptions of
the spectrum, which are so delicate that only the best prisms
will shew them, may be seen in the spectra formed as we
have described.
85. We shall now consider the term
X \b. 7rpe\2
W7rpe Xb s
When p is small, or when e is small, this is= 1. When
p is increased to any multiple of it vanishes. ConseXb
quently, whenever the same value of p is a multiple of
and of -, one of the spectra will disappear: that is,
e +g
whenever e and g are commensurate. This is true in experiment. And at all events, the successive spectra are less
bright than the central colourless image, this term having
its greatest value when p = 0.
It is unnecessary to consider the effect of the first term,
as it only points out the law of brightness in the direction
of the length of the parallelograms.
86. The whole of the experiments which are the subject
of Prop. 20 are easily made by limiting the aperture of the
object glass of a telescope, or by placing gratings before it,
The appearances which we have investigated are those that
would be formed on a screen in the focus of the object glass;
but it is well known by common Optics that the appearance
presented to the eye, when an eye-glass is applied whose
focus coincides with the focus of the object glass, is just
the same as if the light had been received on a screen placed