polite Surface of any pellucid
Medium be reflected back, the Fits of easy Reflexion, which they have at
the point of Reflexion, shall still continue to return; and the Returns
shall be at distances from the point of Reflexion in the arithmetical
progression of the Numbers 2, 4, 6, 8, 10, 12, &c. and between these
Fits the Rays shall be in Fits of easy Transmission._

For since the Fits of easy Reflexion and easy Transmission are of a
returning nature, there is no reason why these Fits, which continued
till the Ray arrived at the reflecting Medium, and there inclined the
Ray to Reflexion, should there cease. And if the Ray at the point of
Reflexion was in a Fit of easy Reflexion, the progression of the
distances of these Fits from that point must begin from 0, and so be of
the Numbers 0, 2, 4, 6, 8, &c. And therefore the progression of the
distances of the intermediate Fits of easy Transmission, reckon'd from
the same point, must be in the progression of the odd Numbers 1, 3, 5,
7, 9, &c. contrary to what happens when the Fits are propagated from
points of Refraction.

PROP. XX.

_The Intervals of the Fits of easy Reflexion and easy Transmission,
propagated from points of Reflexion into any Medium, are equal to the
Intervals of the like Fits, which the same Rays would have, if refracted
into the same Medium in Angles of Refraction equal to their Angles of
Reflexion._

For when Light is reflected by the second Surface of thin Plates, it
goes out afterwards freely at the first Surface to make the Rings of
Colours which appear by Reflexion; and, by the freedom of its egress,
makes the Colours of these Rings more vivid and strong than those which
appear on the other side of the Plates by the transmitted Light. The
reflected Rays are therefore in Fits of easy Transmission at their
egress; which would not always happen, if the Intervals of the Fits
within the Plate after Reflexion were not equal, both in length and
number, to their Intervals before it. And this confirms also the
proportions set down in the former Proposition. For if the Rays both in
going in and out at the first Surface be in Fits of easy Transmission,
and the Intervals and Numbers of those Fits between the first and second
Surface, before and after Reflexion, be equal, the distances of the Fits
of easy Transmission from either Surface, must be in the same
progression after Reflexion as before; that is, from the first Surface
which transmitted them in t