which was 53 deg. 35 , gives the Angles of Refraction of the most and
least refrangible Rays 54 deg. 5 2 , and 53 deg. 4 58 , whose Sines
are 8099 and 7995, the common Angle of Incidence being 31 deg. 15 , and
its Sine 5188; and these Sines in the least round Numbers are in
proportion to one another, as 78 and 77 to 50.
Now, if you subduct the common Sine of Incidence 50 from the Sines of
Refraction 77 and 78, the Remainders 27 and 28 shew, that in small
Refractions the Refraction of the least refrangible Rays is to the
Refraction of the most refrangible ones, as 27 to 28 very nearly, and
that the difference of the Refractions of the least refrangible and most
refrangible Rays is about the 27-1/2th Part of the whole Refraction of
the mean refrangible Rays.
Whence they that are skilled in Opticks will easily understand,[G] that
the Breadth of the least circular Space, into which Object-glasses of
Telescopes can collect all sorts of Parallel Rays, is about the 27-1/2th
Part of half the Aperture of the Glass, or 55th Part of the whole
Aperture; and that the Focus of the most refrangible Rays is nearer to
the Object-glass than the Focus of the least refrangible ones, by about
the 27-1/2th Part of the distance between the Object-glass and the Focus
of the mean refrangible ones.
And if Rays of all sorts, flowing from any one lucid Point in the Axis
of any convex Lens, be made by the Refraction of the Lens to converge to
Points not too remote from the Lens, the Focus of the most refrangible
Rays shall be nearer to the Lens than the Focus of the least refrangible
ones, by a distance which is to the 27-1/2th Part of the distance of the
Focus of the mean refrangible Rays from the Lens, as the distance
between that Focus and the lucid Point, from whence the Rays flow, is to
the distance between that lucid Point and the Lens very nearly.
Now to examine whether the Difference between the Refractions, which the
most refrangible and the least refrangible Rays flowing from the same
Point suffer in the Object-glasses of Telescopes and such-like Glasses,
be so great as is here described, I contrived the following Experiment.
_Exper._ 16. The Lens which I used in the second and eighth Experiments,
being placed six Feet and an Inch distant from any Object, collected the
Species of that Object by the mean refrangible Rays at the distance of
49