t-glass composed of two Glasses
ABED and BEFC, alike convex on the outsides AGD and CHF, and alike
concave on the insides BME, BNE, with Water in the concavity BMEN. Let
the Sine of Incidence out of Glass into Air be as I to R, and out of
Water into Air, as K to R, and by consequence out of Glass into Water,
as I to K: and let the Diameter of the Sphere to which the convex sides
AGD and CHF are ground be D, and the Diameter of the Sphere to which the
concave sides BME and BNE, are ground be to D, as the Cube Root of
KK--KI to the Cube Root of RK--RI: and the Refractions on the concave
sides of the Glasses, will very much correct the Errors of the
Refractions on the convex sides, so far as they arise from the
sphericalness of the Figure. And by this means might Telescopes be
brought to sufficient perfection, were it not for the different
Refrangibility of several sorts of Rays. But by reason of this different
Refrangibility, I do not yet see any other means of improving Telescopes
by Refractions alone, than that of increasing their lengths, for which
end the late Contrivance of _Hugenius_ seems well accommodated. For very
long Tubes are cumbersome, and scarce to be readily managed, and by
reason of their length are very apt to bend, and shake by bending, so as
to cause a continual trembling in the Objects, whereby it becomes
difficult to see them distinctly: whereas by his Contrivance the Glasses
are readily manageable, and the Object-glass being fix'd upon a strong
upright Pole becomes more steady.

Seeing therefore the Improvement of Telescopes of given lengths by
Refractions is desperate; I contrived heretofore a Perspective by
Reflexion, using instead of an Object-glass a concave Metal. The
diameter of the Sphere to which the Metal was ground concave was about
25 _English_ Inches, and by consequence the length of the Instrument
about six Inches and a quarter. The Eye-glass was Plano-convex, and the
diameter of the Sphere to which the convex side was ground was about 1/5
of an Inch, or a little less, and by consequence it magnified between 30
and 40 times. By another way of measuring I found that it magnified
about 35 times. The concave Metal bore an Aperture of an Inch and a
third part; but the Aperture was limited not by an opake Circle,
covering the Limb of the Metal round about, but by an opake Circle
placed between the Eyeglass and the Eye, and perforated in the middle
with a little round hole for the Rays to pas