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.

388 UNDULATORY THEORY OF OPTICS.
shews that common light* does not consist of an indefinite
succession of similar elliptic vibrations.
183. The only supposition that seems able to reconcile
these conclusions is this. Common light consists of successive
series of elliptical vibrations (including in this term plane
and circular vibrations), all the vibrations of each series
being similar to each other, but the vibrations of one series
having no relation to those of another. The number of
vibrations in each series must amount to at least several
hundreds; but the series must be so short that several
hundred series enter the eye in every second of time.
It must be observed that a gradual change in the nature
of the vibrations is inadmissible. If, for instance, we supposed
the vibrations elliptical and supposed the ellipse to revolve
uniformly about its center, it would be found that the vibrations in each plane could be resolved into two whose lengths
of wave were different; and, compounding the corresponding
vibrations in perpendicular planes, we should have two rays
of elliptically-polarized light of different colours.
As a simple instance of our general supposition, suppose
1000 similar vibrations in one plane to be followed by 1000
vibrations, of magnitudes equal to the former, in the plane
at right angles to the former plane; then 1000 in the same
plane as at first, &c. The succession of similar waves would
be sufficient to give all the phenomena of interferences in
perfection. At the same time, no colours would be exhibited
with a crystal and an analyzing plate. For the first series
alone would give rings and colours, but the second would
give rings &c. with intensities exactly complementaryt to
* We have not mentioned here the law discovered by the French philosophers, that if two streams of common light from the same source were polarized
in planes perpendicular to each other, and afterwards brought to the same plane
of polarization, they would not interfere; but if two streams of polarized light
from the same source were treated in the same way, they would interfere. The
fact is, that the observing of rings &c. in crystals is far the best way of making
the experiment: the crystal which has double refraction exhibits the two rays
polarized in perpendicular planes, and the analyzing plate brings them to the
same plane of polarization.
t This is seen in our expressions (155) by putting qc+90~ instead of qp, and
a-900 instead of a.