and 81, and thence by Computation the greatest Angle AXR will be found
40 Degrees and 17 Minutes, and the least Angle AYS 54 Degrees and 7
Minutes.
Suppose now that O [in _Fig._ 15.] is the Spectator's Eye, and OP a Line
drawn parallel to the Sun's Rays and let POE, POF, POG, POH, be Angles
of 40 Degr. 17 Min. 42 Degr. 2 Min. 50 Degr. 57 Min. and 54 Degr. 7 Min.
respectively, and these Angles turned about their common Side OP, shall
with their other Sides OE, OF; OG, OH, describe the Verges of two
Rain-bows AF, BE and CHDG. For if E, F, G, H, be drops placed any where
in the conical Superficies described by OE, OF, OG, OH, and be
illuminated by the Sun's Rays SE, SF, SG, SH; the Angle SEO being equal
to the Angle POE, or 40 Degr. 17 Min. shall be the greatest Angle in
which the most refrangible Rays can after one Reflexion be refracted to
the Eye, and therefore all the Drops in the Line OE shall send the most
refrangible Rays most copiously to the Eye, and thereby strike the
Senses with the deepest violet Colour in that Region. And in like
manner the Angle SFO being equal to the Angle POF, or 42 Degr. 2 Min.
shall be the greatest in which the least refrangible Rays after one
Reflexion can emerge out of the Drops, and therefore those Rays shall
come most copiously to the Eye from the Drops in the Line OF, and strike
the Senses with the deepest red Colour in that Region. And by the same
Argument, the Rays which have intermediate Degrees of Refrangibility
shall come most copiously from Drops between E and F, and strike the
Senses with the intermediate Colours, in the Order which their Degrees
of Refrangibility require, that is in the Progress from E to F, or from
the inside of the Bow to the outside in this order, violet, indigo,
blue, green, yellow, orange, red. But the violet, by the mixture of the
white Light of the Clouds, will appear faint and incline to purple.
[Illustration: FIG. 15.]
Again, the Angle SGO being equal to the Angle POG, or 50 Gr. 51 Min.
shall be the least Angle in which the least refrangible Rays can after
two Reflexions emerge out of the Drops, and therefore the least
refrangible Rays shall come most copiously to the Eye from the Drops in
the Line OG, and strike the Sense with the deepest red in that Region.
And the Angle SHO being equal to the Angle POH, or 54 Gr. 7 Min. shall
be the least Angle, in which the most refrangible Rays after two
Reflexions can emerge out of the Drops; and therefore those Rays shall
96