er of the
Sphere, whereof this Glass is a Segment, be called D, and the
Semi-diameter of the Aperture of the Glass be called S, and the Sine of
Incidence out of Glass into Air, be to the Sine of Refraction as I to R;
the Rays which come parallel to the Axis of the Glass, shall in the
Place where the Image of the Object is most distinctly made, be
scattered all over a little Circle, whose Diameter is _(Rq/Iq) x (S
cub./D quad.)_ very nearly,[H] as I gather by computing the Errors of
the Rays by the Method of infinite Series, and rejecting the Terms,
whose Quantities are inconsiderable. As for instance, if the Sine of
Incidence I, be to the Sine of Refraction R, as 20 to 31, and if D the
Diameter of the Sphere, to which the Convex-side of the Glass is ground,
be 100 Feet or 1200 Inches, and S the Semi-diameter of the Aperture be
two Inches, the Diameter of the little Circle, (that is (_Rq x S
cub.)/(Iq x D quad._)) will be (31 x 31 x 8)/(20 x 20 x 1200 x 1200) (or
961/72000000) Parts of an Inch. But the Diameter of the little Circle,
through which these Rays are scattered by unequal Refrangibility, will
be about the 55th Part of the Aperture of the Object-glass, which here
is four Inches. And therefore, the Error arising from the Spherical
Figure of the Glass, is to the Error arising from the different
Refrangibility of the Rays, as 961/72000000 to 4/55, that is as 1 to
5449; and therefore being in comparison so very little, deserves not to
be considered.

[Illustration: FIG. 27.]

But you will say, if the Errors caused by the different Refrangibility
be so very great, how comes it to pass, that Objects appear through
Telescopes so distinct as they do? I answer, 'tis because the erring
Rays are not scattered uniformly over all that Circular Space, but
collected infinitely more densely in the Center than in any other Part
of the Circle, and in the Way from the Center to the Circumference, grow
continually rarer and rarer, so as at the Circumference to become
infinitely rare; and by reason of their Rarity are not strong enough to
be visible, unless in the Center and very near it. Let ADE [in _Fig._
27.] represent one of those Circles described with the Center C, and
Semi-diameter AC, and let BFG be a smaller Circle concentrick to the
former, cutting with its Circumference the Diameter AC in B, and bisect
AC in N; and by my reckoning, the Density of the Light in any Place B,
will be to its Density in N, as AB to BC; and th