In the third Experiment of this first Part, where the refracting Angle
of the Prism was 62-1/2 Degrees, the half of that Angle 31 deg. 15 min.
is the Angle of Incidence of the Rays at their going out of the Glass
into the Air[F]; and the Sine of this Angle is 5188, the Radius being
10000. When the Axis of this Prism was parallel to the Horizon, and the
Refraction of the Rays at their Incidence on this Prism equal to that at
their Emergence out of it, I observed with a Quadrant the Angle which
the mean refrangible Rays, (that is those which went to the middle of
the Sun's coloured Image) made with the Horizon, and by this Angle and
the Sun's altitude observed at the same time, I found the Angle which
the emergent Rays contained with the incident to be 44 deg. and 40 min.
and the half of this Angle added to the Angle of Incidence 31 deg. 15
min. makes the Angle of Refraction, which is therefore 53 deg. 35 min.
and its Sine 8047. These are the Sines of Incidence and Refraction of
the mean refrangible Rays, and their Proportion in round Numbers is 20
to 31. This Glass was of a Colour inclining to green. The last of the
Prisms mentioned in the third Experiment was of clear white Glass. Its
refracting Angle 63-1/2 Degrees. The Angle which the emergent Rays
contained, with the incident 45 deg. 50 min. The Sine of half the first
Angle 5262. The Sine of half the Sum of the Angles 8157. And their
Proportion in round Numbers 20 to 31, as before.
From the Length of the Image, which was about 9-3/4 or 10 Inches,
subduct its Breadth, which was 2-1/8 Inches, and the Remainder 7-3/4
Inches would be the Length of the Image were the Sun but a Point, and
therefore subtends the Angle which the most and least refrangible Rays,
when incident on the Prism in the same Lines, do contain with one
another after their Emergence. Whence this Angle is 2 deg. 0 . 7 . For
the distance between the Image and the Prism where this Angle is made,
was 18-1/2 Feet, and at that distance the Chord 7-3/4 Inches subtends an
Angle of 2 deg. 0 . 7 . Now half this Angle is the Angle which these
emergent Rays contain with the emergent mean refrangible Rays, and a
quarter thereof, that is 30 . 2 . may be accounted the Angle which they
would contain with the same emergent mean refrangible Rays, were they
co-incident to them within the Glass, and suffered no other Refraction
than that at their Emergence. For, if two equal Refractions, the one at
the Incidence of the Rays on the Prism, the other at their Emergence,
make half the Angle 2 deg. 0 . 7 . then one of those Refractions will
make about a quarter of that Angle, and this quarter added to, and
subducted from the Angle of Refraction of the mean refrangible Rays,
48